$76.47 (32% off) A Mathematical Introduction $61.16 (32% off) Introduction to Mathematical $134.32 (21% off) An Introduction to Mathematical $47.97 (40% off) Mathematical Logic $98.01 (1% off) Fundamentals of Mathematical $48.76 (20% off) A Tour Through Mathematical $30.48 (45% off) A Course on Mathematical $35.00 Mathematical Logic $4.95 My Best Mathematical $310.07 Friendly Introduction

1. A Mathematical Introduction to Logic, Second Edition by Herbert Enderton, Herbert B. Enderton List Price: Price: You Save: US$113.00 US$76.47 US$36.53 (32%) Category: Hardcover (2001-01-05) Publisher: Academic Press ISBN: 0122384520 Sales Rank: 56783 Lowest New Price: $64.84 Lowest Used Price: $59.00 (19 Used Items) Canada | United Kingdom | Germany | France | Japan Product Description A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional coverage of introductory material such as sets. * Increased flexibility of the text, allowing instructors more choice in how they use the textbook in courses. * Reduced mathematical rigour to fit the needs of undergraduate students ... Read more Customer Reviews Average Customer Review: Based on 12 reviews. NOT A GOOD CHOICE FOR THE BUKKAKE LOVER The title says it all. If you are one of the chosen few, you are better off buying a different logic book. Fascinating material, poor proofs Maybe it's because I'm only in undergrad, but I found a lot of the proofs in this book to be incomplete and hard to penetrate. Sometimes he would simply write "induction" and be through with it. That being said, this book covers a lot more material than other logic books, and the majority of it is extremely interesting. Much of it is, again, hard to penetrate (section 2.7 almost made me want to give up), but I found it to be a very worthwhile read. It covers things other authors simply hand-wave away such as the proof for the recursion theorem and the unique-readability theorem. I would recommend this to anyone with suitable mathematical maturity, but don't expect an easy read. For someone at the undergrad level there are better places to start. From the point of a CS student It's very hard to review a book like this without letting personal interest in the subject bias you... but I'll try ;). I used this book in my fourth year at Berkeley. Being a CS major, I found the chapter on sentential (aka boolean) logic very pedantic. I feel that most people are going to be able to easily navigate that part by sheer intuition. On the other hand, first-order logic (the real meat of the course) comes with little motivation from Enderton. He simply dives into the syntax, as if the semmantics will be just as obvious as in sentential logic. One of the main points of this class that I didn't understand until late in the semester, was that mathematical logic is merely an attempt to model (using symbols) the logic most mathematician use proofs, which are written in words. In turn, this gives us a framework to reason about mathematical logic itself, creating a whole new branch of mathematics in its own right (perhaps you can see why it took me a while to understand all this). The only attempt that Enderton makes to explain this is a poorly drawn diagram of "meta-theorems" on top, which are the results of mathematical logic, and theorems, which are the subjects of mathematical logic, on the bottom. The oddest thing about this book was its treatment of algorithms, which is one of the most interesting aspects of this subject. Any (meta)theorems about those were marked with a star, because a precise definition of an algorithm is never given. I'm guessing most reviewers who praise the rigor of this book tend to overlook this weakness, because they come from math departments and not CS departments. If you take a course in computability and complexity theory, you'll see the two subjects are intimately intertwined. This may be the best book on the subject, but I did not feel it guide me very much through the course, esp the later half about first-order logic. John Wilson Keen students may find if they study and parse both editions of Enderton's Logic they may find much of interest. Getting to the root of a problem can be of use in many situations. So best of luck. Moderately difficult and very effective This is the most clear book on intermediate level logic that is available. I have many of the logic books that are on its level, and this one is perfect. It covers the most important, difficult concepts in the easiest way possible. It is above all clear (though very terse). It is easier than Mendelson's quasi-research-problem text but, in my opinion, as it pertains to First Order Logic and Computability Theory, one learns no more through Mendelson's approach. Perhaps its only problem is that it might be just a bit too difficult without an understanding, helpful instructor (or TA) to guide one through the exercises. At any rate an effective progression up to the book might entail: Patty's "Foundations of Higher Mathematics", to Klenk's "Understanding Symbolic Logic", to "Logic, Sets, and Recursion" by Causey. Well, perhaps one might get by with just "Language, Proof, and Logic" by Barwise and Etchemendy. Nonetheless, only after equivalent material has been understood thoroughly can the more mathematical nature of Enderton's book be fully comprehended. And gone at alone on one's free time, such a progression will probably take 2 years, but maybe more. ... Read more Similar Items: 1. Introduction to Logic 2. Elements of Set Theory 3. Introduction to Set Theory, Third Edition, Revised and Expanded (Pure and Applied Mathematics) 4. Set Theory and the Continuum Hypothesis (Dover Books on Mathematics) 5. Abstract Algebra . Favourite Lists: 1. Mathematical Logic. 2. The Basics of Mathematics. 3. My Books. 4. A Formal Methods List for the Theorist and for the Practitioner. 5. Popular Mathematical Logic Texts. 6. Books I own. 7. Mathematical logic and foundations. 8. Stanford CS Comp Reading (based on '02-'03 list). 9. Timeless Logic puzzles from a master mathematician. 10. Beginning mathematics.

2. Introduction to Mathematical Logic, Fifth Edition (Discrete Mathematics and Its Applications) by Elliott Mendelson List Price: Price: You Save: US$89.95 US$61.16 US$28.79 (32%) Category: Hardcover (2009-08-11) Publisher: Chapman and Hall/CRC ISBN: 1584888768 Sales Rank: 257927 Lowest New Price: $39.80 Lowest Used Price: $36.95 (13 Used Items) Canada | United Kingdom | Germany | France | Japan Product Description Retaining all the key features of the previous editions, Introduction to Mathematical Logic, Fifth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The text also discusses the major results of Gödel, Church, Kleene, Rosser, and Turing. New to the Fifth Edition A new section covering basic ideas and results about nonstandard models of number theory A second appendix that introduces modal propositional logic An expanded bibliography Additional exercises and selected answers This long-established text continues to expose students to natural proofs and set-theoretic methods. Only requiring some experience in abstract mathematical thinking, it offers enough material for either a one- or two-semester course on mathematical logic. ... Read more Similar Items: 1. On Formally Undecidable Propositions of Principia Mathematica and Related Systems 2. Godel's Theorem: An Incomplete Guide to Its Use and Abuse 3. Introduction to Logic 4. Set Theory and the Continuum Problem (Dover Books on Mathematics) 5. Gödel's Proof . Favourite Lists: 1. Mathematical Logic.

3. An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof (Applied Logic Series) by Peter B. Andrews List Price: Price: You Save: US$169.00 US$134.32 US$34.68 (21%) Category: Hardcover (2002-07-31) Publisher: Springer ISBN: 1402007639 Sales Rank: 599423 Lowest New Price: $134.16 Lowest Used Price: $134.00 (9 Used Items) Canada | United Kingdom | Germany | France | Japan Product Description This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification. ... Read more Customer Reviews Average Customer Review: Based on 1 reviews. used early draft as grad text I took a great graduate course from Prof. Andrews, way back in the 1970's, where his class lecture notes were titled "To Truth Through Proof", so I assume that was a very very early draft of this book. If so, this must be a very good book, because his notes were wonderful even back then. ... Read more Similar Items: 1. An Introduction to the Theory of Numbers 2. First Course in Abstract Algebra, A (3rd Edition) 3. ML for the Working Programmer 4. Data Structures and Problem Solving Using Java (3rd Edition) 5. Introduction to Algorithms, Third Edition .

4. Mathematical Logic (Undergraduate Texts in Mathematics) by H.-D. Ebbinghaus, J. Flum, W. Thomas List Price: Price: You Save: US$79.95 US$47.97 US$31.98 (40%) Category: Hardcover (1994-06-10) Publisher: Springer ISBN: 0387942580 Sales Rank: 535406 Lowest New Price: $47.96 Lowest Used Price: $32.19 (21 Used Items) Canada | United Kingdom | Germany | France | Japan Product Description This junior/senior level text is devoted to a study of first-order logic and its role in the foundations of mathematics: What is a proof? How can a proof be justified? To what extent can a proof be made a purely mechanical procedure? How much faith can we have in a proof that is so complex that no one can follow it through in a lifetime? The first substantial answers to these questions have only been obtained in this century. The most striking results are contained in Goedel's work: First, it is possible to give a simple set of rules that suffice to carry out all mathematical proofs; but, second, these rules are necessarily incomplete - it is impossible, for example, to prove all true statements of arithmetic. The book begins with an introduction to first-order logic, Goedel's theorem, and model theory. A second part covers extensions of first-order logic and limitations of the formal methods. The book covers several advanced topics, not commonly treated in introductory texts, such as Trachtenbrot's undecidability theorem. Fraissé's elementary equivalence, and Lindstroem's theorem on the maximality of first-order logic. ... Read more Customer Reviews Average Customer Review: Based on 12 reviews. Will not suggest to anyone. Not a very good text for beginners. There are other good books like the ones by Mendelson, A. Margaris and tons of others. Excellent Choice for Teaching Mathematical Logic This is a truly excellent book -- one I've used (along with other other books) to teach mathematical logic for 20 years. (The new edition provided welcome coverage of logic programming.) Traditionally, logic pedagogy has tended to revolve around which colleges or universities are involved. You will need to have sharp students to take full advantage of this textbook. In addition, some proof construction environment/proof checker is a good thing to have accompany the textbook; the same would hold of model finders. For grad students in my lab, I require familiarity with the book, sooner or later. The steepest on-ramp to the fast lane of logic Learning mathematical logic from this textbook is a little like learning to rock-climb by going straight to the half-dome. Most likely, you'll fall to your death. But if you're strong enough and lucky enough to endure the climb, you'll look back on how far you've come and have an "OH MY GOD I ACTUALLY DID THAT???" moment of clarity like nothing else you've ever experienced :-) Should be the standard undergrad introduction Intended for a one-semester course, it ignores some of the usual topics in a survey course so it can give a deeper treatment of the nature and adequacy of mathematical proofs. It slights number theory, second-order logic, nonstandard analysis, and set theory. There is only enough on recursion and computability to support the main topic, but it goes deeper than usual on limitative results. What it does cover it does very well. Motivation is rich and exercises follow well from the text. Proofs are very clear. Overall, there is much greater coherence in the development of ideas than you usually see in a survey text. While the writing is very good, there is a shortage of definitions, examples, and exercises. Notation is not always clearly introduced and they adopt so many abbreviations it's hard to keep track of what things mean. I also thought that it was not as clear in the second half, maybe due to the multiple authors. Still, I would choose it over Enderton unless you need lots of exercises for class use. Reads like Mathematical Poetry As others have pointed out, this book is not for beginners, but is very well suited for those with some confidence in formal logic and axiomatized set theory. The book is just great if you want to deepen your understanding of the subject beyond what can be had from undergrad level courses on the topic. It should be required reading for any student of computational logic. The question this book addresses is not "why logic?", or "what is a formal logic?", but more specifically, "why is first-order predicate calculus with equality such a good foundation for mathematics?" The formal mathematics is organized and presented so clearly and precisely that I felt I was admiring a fine crystal structure. The notation used may seem excessive to some, but it actually is the least amount of notation that could be gotten away with without resorting to glossing over fine distinctions. For example, many logic books assume a fixed countably infinite number of function and predicate symbols, which leads to some confusion when comparing different axiomatizations of the natural numbers, or of groups. This book on the other hand is crystal clear on how such different axiomatizations are related to each other. Another subtle point I never noticed before about first-order predicate logic but that is pointed out in the footnote on page 73 is that one might think it possible that just because a formula can be proven with one choice of predicate and function symbols, it might not be provable with a different choice of symbols. It turns out that this cannot happen as a simple consequence of the completeness theorem! (p. 85) The book explores second-order predicate logic and makes explicit some of the difficulties, such as incompleteness and even the problem of how closely the truth of a formula in second order logic depends on what we take as true in set theory: different axiomatizations of set theory lead to different semantics for second-order predicate logic! There is a great chapter on the incompleteness theorems, and in addition to Goedel's theorems, there is a section on Register Machines (a version of Turing Machines) and a proof of the undecidability of arithmetic using the halting problem, as well as a more general theorem about the undecidability of any theory that can encode the workings of a Register Machine. The next section is a reasonable presentation of the mathematical underpinnings of logic programming. The book concludes with an algebraic characterization of elementary equivalence followed by two deep theorems by Lindstrom that demonstrate the uniqueness of first order predicate calculus among formal languages with set theoretic semantics. ... Read more Similar Items: 1. Introduction to Logic 2. First-Order Logic 3. A Mathematical Introduction to Logic, Second Edition 4. Set Theory and the Continuum Hypothesis (Dover Books on Mathematics) 5. Introduction to Metamathematics . Favourite Lists: 1. Mathematical Logic. 2. Popular Mathematical Logic Texts. 3. mathematical logic. 4. "A list of some of my favorite math books".

5. Fundamentals of Mathematical Logic by Peter G. Hinman List Price: Price: You Save: US$99.00 US$98.01 US$0.98999999999999 (1%) Category: Hardcover (2005-11-15) Publisher: A K Peters Ltd ISBN: 1568812620 Sales Rank: 667318 Lowest New Price: $98.01 Lowest Used Price: $85.65 (12 Used Items) Canada | United Kingdom | Germany | France | Japan Customer Reviews Average Customer Review: Based on 2 reviews. Where's the proof? Quoting the author Hinman (page xi): "A notable lacuna is Proof Theory, which fails to appear largely due to the incompetence of the author in this area". And he is correct: there is no proof theory in this book, no Hilbert axioms, no Gentzen natural deduction nor sequent calculus, nothing (except for a cursory 13 page section out of 878). So, on the one hand, we have the largest logic book I have ever seen -- and yet, ironically, the most incomplete. I'm sure there's a lot of good stuff in this book and it is written well but it's missing half the story, i.e., it is missing an exposition of how one manipulates symbols formally to prove theorems. Even the semantic, model-theoretic side is incomplete: there's no semantic tableaux, no resolution. Also, at 878 pages, plausibly a considerable portion is at an advanced level. So, this is not a good introduction to logic. By far the best introduction to logic I've found is "Mathematical Logic for Computer Science" by Mordechai Ben-Ari. Serious/pure mathematicians of course will want to continue with the likes of "An Introduction To Mathematical Logic" by Elliott Mendelson. A Comprehensive Graduate Text If I were a young graduate student in mathematics looking for that one "perfect" graduate text on mathematical logic to purchase with my (very) limited income, I would buy a copy of Professor Hinman's book. In just under 900 pages, Hinman provides an extremely well written and informed introduction to propositional logic, first order mathematical logic, axiomatic set theory, model theory, and recursion theory. Indeed, the book is written so well that a motivated student with the requisite background can easily profit from independent study---a statement that simply cannot be made about many of the other "classic" references in this difficult field. One great virtue of having a single reference that introduces these diverse but interconnected areas is the uniformity of notation and definitions; the reader need not pull his hair out cross-referencing between texts that use wildly different notation and, occasionally, different definitions. I studied mathematical logic at the University of Colorado--Boulder in the late 1970s. In those days, the logic students all depended on a standard list of references to prepare for the PhD qualifying examinations, and it is significant that all or nearly all of those works are still in print. At the introductory level we read the magnificent books on mathematical logic and set theory by Herbert Enderton. At the graduate level, we read Shoenfield, Monk, Mendelson, and Manin for mathematical logic, Chang and Keisler for Model Theory, Jech (and to a lesser extent, Kunen) for set theory, and Hartley Rogers for recursive function theory. In the course of plodding through these references, I discovered a wonderful comprehensive text by John Bell and Moshe Machover and quickly elevated it to primary status on my reading list. Bell and Machover remains my favorite among the older references today, nearly thirty years later, both in terms of comprehensive coverage and clarity of prose; when I reach for a reference to clarify an issue on foundations, Bell and Machover is the first book I turn to. The new book by Hinman achieves the same comprehensive goals of Bell and Machover, providing a rigorous and coordinated introduction to logic, set theory, recursion theory and model theory. However, Hinman incorporates some research topics that have emerged in the years since the 1977 publication of Bell and Machover, and it includes some more traditional topics that were difficult to find in the earlier texts. To give one example, Hinman provides a brief introduction to the axiom of determinacy. This topic was made available to non-specialists in two papers published in the AMS Notices of June and July, 2001, where Hugh Woodin of Berkeley discussed the axiom of projective determinacy and other hypotheses within the context of possible enlargements of ZFC that would resolve Cantor's famous continuum hypothesis. A second example is Hinman's very lucid treatment of forcing; this writer has always had difficulty understanding the very few presentations of Paul Cohen's forcing technique that have been available in the older texts, but I found Hinman's treatment exceptionally clear and easy to follow. Professor Hinman states that this book resulted from his nearly 40 years of experience teaching mathematical logic to graduates and undergraduates. The truth of this claim is reflected in the exceptional clarity of the prose and the coherence as one skims across different chapters. It is apparent that serious thought, consideration for the reader, and years of experience in the classroom shaped the final form of this text. Given the paucity of new texts in mathematical logic and foundations, the publication of this book is truly a cause for celebration. If you can only afford one text on the subject, purchase this one; if you are burdened with an abundance of spare change, I recommend buying Bell and Machover as a second reference to supplement Hinman. ... Read more Similar Items: 1. Mathematical Logic 2. A Mathematical Introduction to Logic, Second Edition 3. Model Theory (Encyclopedia of Mathematics and its Applications) 4. Algebra 5. Principles of Mathematical Analysis, Third Edition . Favourite Lists: 1. Mathematical Logic. 2. The History of Philosophy and Logic. 3. Physical Sciences Study guide!!. 4. Logic for Philosophy Grad Students.

6. A Tour Through Mathematical Logic (Carus Mathematical Monographs) by Robert S. Wolf List Price: Price: You Save: US$60.95 US$48.76 US$12.19 (20%) Category: Paperback (2005-01-08) Publisher: The Mathematical Association of America ISBN: 0883850362 Sales Rank: 572856 Lowest New Price: $48.76 Lowest Used Price: $54.90 (10 Used Items) Canada | United Kingdom | Germany | France | Japan Product Description This book provides a tour through the main branches of the foundations of mathematics. It contains chapters covering elementary logic, basic set theory, recursion theory, Gödel’s (and others’) incompleteness theorems, model theory, independence results in set theory, nonstandard analysis, and constructive mathematics. In addition, this monograph discusses several topics not normally found in books of this type, such as fuzzy logic, nonmonotonic logic, and complexity theory. The word "tour" in the title deserves some explanation. This word is meant to emphasize that this is not a textbook in the strict sense. To be sure, it has many of the features of a textbook, including exercises. But it is less structured, more free-flowing, than a standard text. It also lacks many of the details and proofs that one normally expects in a mathematics text. However, in almost all such cases there are references to more detailed treatments and the omitted proofs. Therefore, this book is actually quite suitable for use as a text at the university level (undergraduate or graduate), provided that the instructor is willing to provide supplementary material from time to time. The most obvious advantage of this omission of detail is that this monograph is able to cover a lot more material than if it were a standard textbook of the same size. This de-emphasis on detail is also intended to help the reader concentrate on the big picture, the essential ideas of the subject, without getting bogged down in minutiae. This book could have been titled "A Survey of Mathematical Logic," but the author’s choice of the word "tour" was deliberate. A survey sounds like a rather dry activity, carried out by technicians with instruments. Tours, on the other hand, are what people take on their vacations. They are intended to be fun. The goal of this book is similar: to provide an introduction to the foundations of mathematics that is substantial and stimulating, and at the same time a pleasure to read. It is designed so that any interested reader with some post-calculus experience in mathematics should be able to read it, enjoy it, and learn from it. ... Read more Customer Reviews Average Customer Review: Based on 1 reviews. An in-depth and in-breadth tour of the foundations of mathematics This tour is both broad and deep; it covers most of what would ordinarily be considered upper level material in the foundations of mathematics. While it contains theorems, proofs and exercises, it does not have the structure of a textbook. It is more on the order of an advanced survey that includes history. There are occasional short sections reserved for biographies of mathematicians of note in the field. For example, there are biographies of Bertrand Russell, Euclid, Georg Cantor, John von Neumann and Julia Robinson. The chapter headings are: *) Predicate logic *) Axiomatic set theory *) Recursion theory and computability *) Godel's incompleteness theorems *) Model theory *) Contemporary set theory *) Nonstandard analysis *) Constructive mathematics Given the branching away from logic into set theory and analysis, in my opinion, this book is best considered a survey of the foundations of mathematics. Considered in that way, it is a sound primer for people with mathematical maturity. If you have an interest in advanced material in these areas, you will find this book worthy of study. ... Read more Similar Items: 1. Set Theory and the Continuum Problem (Dover Books on Mathematics) 2. The Foundations of Mathematics (Logic) 3. A Course in Mathematical Logic for Mathematicians (Graduate Texts in Mathematics) 4. Roads to Infinity: The Mathematics of Truth and Proof 5. Set Theory and the Continuum Hypothesis (Dover Books on Mathematics) . Favourite Lists: 1. Mathematical Logic. 2. The History of Philosophy and Logic.

7. A Course on Mathematical Logic (Universitext) by Shashi Mohan Srivastava List Price: Price: You Save: US$54.95 US$30.48 US$24.47 (45%) Category: Paperback (2008-03-12) Publisher: Springer ISBN: 0387762752 Sales Rank: 1447036 Lowest New Price: $30.48 Lowest Used Price: $24.49 (8 Used Items) Canada | United Kingdom | Germany | France | Japan Product Description This is a short, distinctive, modern, and motivated introduction to mathematical logic for senior undergraduate and beginning graduate students in mathematics and computer science. Any mathematician who is interested in knowing what logic is concerned with and who would like to learn Gödel’s incompleteness theorems should find this book particularly convenient. The treatment is thoroughly mathematical, and the entire subject has been approached like a branch of mathematics. Serious efforts have been made to make the book suitable for the classroom as well as for self-reading. The book does not strive to be a comprehensive encyclopedia of logic. Still, it gives essentially all the basic concepts and results in mathematical logic. The book prepares students to branch out in several areas of mathematics related to foundations and computability such as logic, axiomatic set theory, model theory, recursion theory, and computability. The main prerequisite for this book is the willingness to work at a reasonable level of mathematical rigor and generality. ... Read more Similar Items: 1. Roads to Infinity: The Mathematics of Truth and Proof 2. A Course in Mathematical Logic for Mathematicians (Graduate Texts in Mathematics) 3. A Concise Introduction to Mathematical Logic (Universitext) 4. Sets, Logic and Maths for Computing (Undergraduate Topics in Computer Science) 5. Elementary Induction on Abstract Structures (Dover Books on Mathematics) . Favourite Lists: 1. Mathematical Logic.

8. Mathematical Logic by Joseph R. Shoenfield List Price: Price: US$35.00 US$35.00 Category: Paperback (2001-01-15) Publisher: AK Peters, Ltd. ISBN: 1568811357 Sales Rank: 153026 Lowest New Price: $34.83 Lowest Used Price: $29.75 (10 Used Items) Canada | United Kingdom | Germany | France | Japan Product Description Starting with the concept that mathematical logic is not a collection of vaguely related results, but a method of attacking some of the most interesting problems which face the mathematician, the author sets the tone for this classic introduction. The basic concepts are presented in an unusually clear and accessible fashion, keeping in mind the original purpose of mathematical logic to build the foundations of this vast edifice of knowledge in a way that helps and intrigues the working mathematician as much as the philosophically minded student of logic. This book has served as a rite of passage to many mature and accomplished researchers. ... Read more Features: ISBN13: 9781568811352 Condition: New Notes: BUY WITH CONFIDENCE, Over one million books sold! 98% Positive feedback. Compare our books, prices and service to the competition. 100% Satisfaction Guaranteed Customer Reviews Average Customer Review: Based on 2 reviews. Standard by default Almost four decades after being written, this is still the standard graduate survey text. A large part of the reason is that there is little competition, but it is also a good book on its own merits. The author writes with a clarity and concision you rarely see in a math (or any) textbook. Proofs are straighforward, not tricky or convoluted. There are many excercises and with detailed setup. The exercises are often quite hard, requiring significant extension from the text. Although the writing is good, that doesn't mean it is easy. He progresses deliberately through the details, rarely giving an overview. I think he is just expecting that you already have a good sense of context from the undergrad logic course you took (didn't you?). Sometimes he seems to belabor a point. There is also a dearth of examples, just five in the whole book, three of them in the appendix. There are no references at all. The age of the book makes it, not wrong, but inadequate in some areas. Still, I have looked at alternatives and haven't found something better for a graduate survey text in English. Rock-solid introduction to Mathematical Logic Since my first contact with mathematical logic, I've always seen it as a kind of brainwashing, forcing one's mind to work based on several little pieces of thought. Nevertheless, it can be described as "a necessary evil", because the mindless use of mathematical logic throughout mathematics is very treacherous, as it can be seen in the problems regarding the axiom of choice, the Banach-Tarski paradox in measure theory, the issues about the undecidability of certain assumptions in set theory, and the very limitations of mathematical logic. Usually, of course, most work in mathematics doesn't require a deep knowledge of rigorous mathematical logic, but it's always a good thing to a serious mathematician to have some acquaintance with it, even if it's just to avoid boobytraps. Then, it's hard to find a better choice than Shoenfield's book. After a long absence from the book market, A K Peters made the wise decision of reprint this masterpiece. Although most of its contents are fairly standard for a book on mathematical logic (unlike the equally marvellous out-of-print book of Yu. I. Manin, which has a more philosophical slant and concerns itself with issues such as quantum logic, literature, etc.), it provides proofs for many propositions that in most of the literature are only stated. It has, of course, some extras not generally found in other books, as for example issues concerning constructibility of sets. But the most important characteristic of this book is its clarity and precision. It doesn't waste time in unnecessary stuff, and shows why we need mathamatical logic at all. Although it lacks some topics (for example, it doesn't discuss other axiomatic set theories besides Zermelo-Fraenkel. This is not so nice, because it lacks the distinction between classes and sets, one of the tenets of the Goedel- -Bernays-von Neumann set theory, although it is conceptually easier than this last one. But maybe it's a pedagogical choice, because the set theory we all intuitively know is more or less based in Zermelo-Fraenkel), its main concern is pedagogy, so this limitation has a sound reason: this book exposes mainly the logic present in the math most mathematicians and alike scientists (mathematical physicists, etc.) use. Its solidity and razor-sharp precision is great to instruct these people to be more careful with the math they use. Besides that, some of the missing topics can be complemented by Mendelsson's "Introduction to Mathematical Logic", which is a bit more "merciful" book, which, by the other side, welcomes the thoroughness of Shoenfield. ... Read more Similar Items: 1. Set Theory and the Continuum Hypothesis (Dover Books on Mathematics) 2. Fundamentals of Mathematical Logic 3. General Topology 4. Model Theory: An Introduction 5. Principles of Mathematical Analysis, Third Edition . Favourite Lists: 1. Mathematical Logic. 2. Books Cited in Other Reviews and in Comments. 3. Logic for Philosophy Grad Students. 4. Popular Mathematical Logic Texts. 5. Mathematical logic and foundations. 6. Mathematical logic. 7. mathematical logic.

9. My Best Mathematical and Logic Puzzles (Math & Logic Puzzles) by Martin Gardner List Price: Price: US$4.95 US$4.95 Category: Paperback (1994-11-01) Publisher: Dover Publications ISBN: 0486281523 Sales Rank: 15187 Lowest New Price: $1.65 Lowest Used Price: $1.47 (16 Used Items) Canada | United Kingdom | Germany | France | Japan Product Description Noted expert selects 70 "short" puzzles. The Returning Explorer, The Mutilated Chessboard, Scrambled Box Tops, and 67 more. Solutions included. ... Read more Features: ISBN13: 9780486281520 Condition: New Notes: BUY WITH CONFIDENCE, Over one million books sold! 98% Positive feedback. Compare our books, prices and service to the competition. 100% Satisfaction Guaranteed Customer Reviews Average Customer Review: Based on 13 reviews. Fun book to bring on vacation This is a must bring when you go on vacation and just need some time to chill at the beach or at the end of a busy day, in between day and evening plans. If you happen to be interviewing in the technical fields you may run across interviewers that ask brain teasers. You'll find many of those problems in this book. For technical interviewing this makes a good study guide. I have collected quite a few puzzle books and was never fully satisfied with any of them until I heard about the authoer and decided to pick up one his books. The puzzles are all differnt from each other, ranging from word problems to geometry problems.The solutions given are very complete and actually take up the largest emphasis. Very good puzzles book I didn't expect much from a 5-dollar book, but I was pleasantly surprised. Other reviewers have already covered the quality of the book, so I won't go into those details, but I have the following suggestion for you. Store this item in your wishlist and use it when you need a filler item to qualify for free shipping. Highly recommend the book. Don't waste your money While the puzzles are intriguing and thought-provoking, the solutions don't explain how the answers were reached. I was highly disappointed. Great bathroom reading! Very nice. I like the old-fashioned approach (I think the author has been writing books like this since the 1960s) and the problems are interesting and varied; most of them you can do in your head (hence an ideal "bathroom book") but some do make you break out the pencil and paper just to double-check. Highly recommended for interested people who studied Maths to around age 18 or beyond. Good for warming up your brain. Nice collection of puzzles with varying difficulties, which do not require any special knowledge of mathematics. ... Read more Similar Items: 1. Entertaining Mathematical Puzzles 2. Perplexing Puzzles and Tantalizing Teasers (Math & Logic Puzzles) 3. Entertaining Science Experiments with Everyday Objects 4. The Moscow Puzzles: 359 Mathematical Recreations (Math & Logic Puzzles) 5. The Colossal Book of Short Puzzles and Problems . Favourite Lists: 1. Riddles, logic puzzles, brain teasers. 2. Meyerholz Logic Club. 3. Art, Math and Science. 4. Problems and Puzzles. 5. Tutoring. 6. Freaks and Geeks. 7. Suggested Math Readings. 8. Things that Keep Me from Watching Too Much TV. 9. Martin Gardner Puzzle Books. 10. Great Puzzle Books.

10. Friendly Introduction to Mathematical Logic, A by Christopher C. Leary List Price: $76.00 Category: Hardcover (1999-12-08) Publisher: Prentice Hall ISBN: 0130107050 Sales Rank: 676693 Lowest New Price: $310.07 Lowest Used Price: $56.93 (12 Used Items) Canada | United Kingdom | Germany | France | Japan Product Description This user-friendly introduction to the key concepts of mathematical logic focuses on concepts that are used by mathematicians in every branch of the subject. Using an assessible, conversational style, it approaches the subject mathematically (with precise statements of theorems and correct proofs), exposing readers to the strength and power of mathematics, as well as its limitations, as they work through challenging and technical results. KEY TOPICS: Structures and Languages. Deductions. Comnpleteness and Compactness. Incompleteness--Groundwork. The Incompleteness Theorems. Set Theory. : For readers in mathematics or related fields who want to learn about the key concepts and main results of mathematical logic that are central to the understanding of mathematics as a whole. ... Read more Customer Reviews Average Customer Review: Based on 2 reviews. Why is this out of print? The impossible goal of this text is to start from scratch and then cover both incompleteness theorems in a single semester, and under his presentation it would almost be manageable. This is by far the best written text on predicate calculus I have read. Kaye and Goldrei can't really compare, as they contain less material and what they do cover isn't done quite as well. Enderton on the other hand covers more than Leary, but is much more dense and would not serve as well as an introduction. The main drawback of the book is how much effort the author put into making it fit into a single semester. There is a lot of fascinating material that could have been covered in greater depth than is done. It is worth noting that he almost completely skips over propositional calculus, so if you find yourself struggling at the beginning of the book you may want to read up on that subject in another text (the first half of Goldrei would do nicely). Also the section on the second incompleteness theorem is extremely rushed; some of the properties of peano arithmetic used for the proof are not proven. Still, it's better than the other options I've seen. You would think with all the mediocre mathematics texts Dover picks up they would have found this gem. Most Accessible Undergraduate Text Covering Incompleteness I have used this text in both graduate and undergraduate courses as well as tutorials and independent studies. It is the best text for a one semester course that introduces formal logic and has as its goal the Incompleteness Theorems of Godel. Students have reported it to be very readable and the array of exercises is excellent. Moreover, the author is a really nice fellow. ... Read more Similar Items: 1. Calculus, 4th edition 2. Axiomatic Set Theory 3. Set Theory and the Continuum Hypothesis (Dover Books on Mathematics) 4. Classic Set Theory for Guided Independent Study (Chapman & Hall Mathematics) 5. An Introduction to Non-Classical Logic: From If to Is (Cambridge Introductions to Philosophy) . Favourite Lists: 1. Essential Books of Mathematics.