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1. Mathematical Logic, 2nd Edition (Undergraduate Texts in Mathematics) by H.D. Ebbinghaus, J. Flum, Wolfgang Thomas
Product Description This introduction to firstorder logic clearly works out the role of firstorder logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theoremproving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of firstorder logic, and the fundamentals of logic programming.
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2. A Beginner's Further Guide to Mathematical Logic by Raymond M. Smullyan
Product Description This book is a sequel to my Beginner's Guide to Mathematical Logic.The previous volume deals with elements of propositional and firstorder logic, contains a bit on formal systems and recursion, and concludes with chapters on Gödel's famous incompleteness theorem, along with related results.The present volume begins with a bit more on propositional and firstorder logic, followed by what I would call a "fein" chapter, which simultaneously generalizes some results from recursion theory, firstorder arithmetic systems, and what I dub a "decision machine." Then come five chapters on formal systems, recursion theory and metamathematical applications in a general setting. The concluding five chapters are on the beautiful subject of combinatory logic, which is not only intriguing in its own right, but has important applications to computer science. Argonne National Laboratory is especially involved in these applications, and I am proud to say that its members have found use for some of my results in combinatory logic.This book does not cover such important subjects as set theory, model theory, proof theory, and modern developments in recursion theory, but the reader, after studying this volume, will be amply prepared for the study of these more advanced topics.
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3. A Beginner's Guide to Mathematical Logic (Dover Books on Mathematics) by Raymond M. Smullyan
Product Description Written by a creative master of mathematical logic, this introductory text combines stories of great philosophers, quotations, and riddles with the fundamentals of mathematical logic. Author Raymond Smullyan offers clear, incremental presentations of difficult logic concepts. He highlights each subject with inventive explanations and unique problems.
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4. My Best Mathematical and Logic Puzzles (Dover Recreational Math) by Martin Gardner
Product Description Over a period of 25 years as author of the Mathematical Games column for Scientific American, Martin Gardner devoted a column every six months or so to short math problems or puzzles. He was especially careful to present new and unfamiliar puzzles that had not been included in such classic collections as those by Sam Loyd and Henry Dudeney. Later, these puzzles were published in book collections, incorporating reader feedback on alternate solutions or interesting generalizations.
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Similar Items: 1. The Moscow Puzzles: 359 Mathematical Recreations (Dover Recreational Math) 2. Of Course!: The Greatest Collection of Riddles & Brain Teasers For Expanding Your Mind 3. Entertaining Mathematical Puzzles 4. Perplexing Puzzles and Tantalizing Teasers (Dover Children's Activity Books) 5. The Stanford Mathematics Problem Book: With Hints and Solutions (Dover Books on Mathematics) 6. Challenging Logic Puzzles 7. Entertaining Science Experiments with Everyday Objects 8. Martin Gardner's Science Magic: Tricks and Puzzles (Dover Magic Books) 9. The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems 10. 100 Math Brainteasers (Grade 7, 8, 9, 10). Arithmetic, Algebra and Geometry Brain Teasers, Puzzles, Games and Problems with Solutions: Math olympiad contest problems for elementary and middle schools . 
5. Mathematical Logic (Dover Books on Mathematics) by Stephen Cole Kleene
Product Description Undergraduate students with no prior classroom instruction in mathematical logic will benefit from this evenhanded multipart text. It begins with an elementary but thorough overview of mathematical logic of first order. The treatment extends beyond a single method of formulating logic to offer instruction in a variety of techniques: model theory (truth tables), Hilberttype proof theory, and proof theory handled through derived rules.
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6. Mathematical Logic (Oxford Texts in Logic) by Ian Chiswell, Wilfrid Hodges
Product Description Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for firstorder logic. At each stage of the text, the reader is given an intuition based on standard mathematical practice, which is subsequently developed with clean formal mathematics. Alongside the practical examples, readers learn what can and can't be calculated; for example the correctness of a derivation proving a given sequent can be tested mechanically, but there is no general mechanical test for the existence of a derivation proving the given sequent. The undecidability results are proved rigorously in an optional final chapter, assuming Matiyasevich's theorem characterising the computably enumerable relations. Rigorous proofs of the adequacy and completeness proofs of the relevant logics are provided, with careful attention to the languages involved. Optional sections discuss the classification of mathematical structures by firstorder theories; the required theory of cardinality is developed from scratch. Throughout the book there are notes on historical aspects of the material, and connections with linguistics and computer science, and the discussion of syntax and semantics is influenced by modern linguistic approaches. Two basic themes in recent cognitive science studies of actual human reasoning are also introduced. Including extensive exercises and selected solutions, this text is ideal for students in logic, mathematics, philosophy, and computer science.
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7. Mathematical Logic (AddisonWesley Series in Logic) by Joseph R. Shoenfield
Product Description This classic introduction to the main areas of mathematical logic provides the basis for a first graduate course in the subject. It embodies the viewpoint that mathematical logic is not a collection of vaguely related results, but a coherent method of attacking some of the most interesting problems, which face the mathematician. The author presents the basic concepts in an unusually clear and accessible fashion, concentrating on what he views as the central topics of mathematical logic: proof theory, model theory, recursion theory, axiomatic number theory, and set theory. There are many exercises, and they provide the outline of what amounts to a second book that goes into all topics in more depth. This book has played a role in the education of many mature and accomplished researchers.
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Similar Items: 1. Introduction to Metamathematics 2. Mathematical Logic (Dover Books on Mathematics) 3. FirstOrder Logic (Dover Books on Mathematics) 4. Logic for Computer Science: Foundations of Automatic Theorem Proving, Second Edition (Dover Books on Computer Science) 5. Real & Complex Analysis 6. Principles of Mathematical Analysis 7. An Introduction to NonClassical Logic: From If to Is (Cambridge Introductions to Philosophy) 8. A Concise Introduction to Mathematical Logic (Universitext) 9. Naming and Necessity 10. Naive Set Theory . 
8. An Introduction to Mathematical Logic (Dover Books on Mathematics) by Richard E. Hodel
Product Description Widely praised for its clarity and thorough coverage, this comprehensive overview of mathematical logic is suitable for readers of many different backgrounds. Designed primarily for advanced undergraduates and graduate students of mathematics, the treatment also contains much of interest to advanced students in computer science and philosophy. An introductory section prepares readers for successive chapters on propositional logic and firstorder languages and logic. Subsequent chapters shift in emphasis from an approach to logic from a mathematical point of view to the interplay between mathematics and logic. Topics include the theorems of Gödel, Church, and Tarski on incompleteness, undecidability, and indefinability; a rigorous treatment of recursive functions and recursive relations; computability theory; and Hilbert's Tenth Problem. Numerous exercises appear throughout the text, and an appendix offers helpful background on number theory.
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9. A Course in Mathematical Logic for Mathematicians (Graduate Texts in Mathematics) by Yu. I. Manin
Product Description 1. The ?rst edition of this book was published in 1977. The text has been well received and is still used, although it has been out of print for some time. In the intervening three decades, a lot of interesting things have happened to mathematical logic: (i) Model theory has shown that insights acquired in the study of formal languages could be used fruitfully in solving old problems of conventional mathematics. (ii) Mathematics has been and is moving with growing acceleration from the settheoretic language of structures to the language and intuition of (higher) categories, leaving behind old concerns about in?nities: a new view of foundations is now emerging. (iii) Computer science, a nononsense child of the abstract computability theory, has been creatively dealing with old challenges and providing new ones, such as the P/NP problem. Planning additional chapters for this second edition, I have decided to focus onmodeltheory,the conspicuousabsenceofwhichinthe ?rsteditionwasnoted in several reviews, and the theory of computation, including its categorical and quantum aspects. The whole Part IV: Model Theory, is new. I am very grateful to Boris I. Zilber, who kindly agreed to write it. It may be read directly after Chapter II. The contents of the ?rst edition are basically reproduced here as Chapters I–VIII. Section IV.7, on the cardinality of the continuum, is completed by Section IV.7.3, discussing H. Woodin’s discovery.
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10. Mathematical Logic for Computer Science by Mordechai BenAri
Product Description Mathematical Logic for Computer Science is a mathematics textbook with theorems and proofs, but the choice of topics has been guided by the needs of students of computer science. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and easy to understand. The uniform use of tableauxbased techniques facilitates learning advanced logical systems based on what the student has learned from elementary systems. The logical systems presented are: propositional logic, firstorder logic, resolution and its application to logic programming, Hoare logic for the verification of sequential programs, and linear temporal logic The third edition has been entirely rewritten and includes new chapters on central topics of modern computer science: SAT solvers and model checking.
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Similar Items: 1. The Algorithm Design Manual 2. Artificial Intelligence: A Modern Approach (3rd Edition) 3. Introduction to Algorithms, 3rd Edition (MIT Press) 4. Logic for Computer Science: Foundations of Automatic Theorem Proving, Second Edition (Dover Books on Computer Science) 5. Logic in Computer Science: Modelling and Reasoning about Systems 6. Certified Programming with Dependent Types: A Pragmatic Introduction to the Coq Proof Assistant (MIT Press) 7. The Lambda Calculus. Its Syntax and Semantics (Studies in Logic) 8. Types and Programming Languages (MIT Press) 9. Intuitionistic Set Theory (Studies in Logic) 10. Three Views of Logic: Mathematics, Philosophy, and Computer Science . 
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