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    $23.05 (8% off)
    Mathematical Logic
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    1. Mathematical Logic (Dover Books on Mathematics)
    by Stephen Cole Kleene
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    US$24.95Dover Publications97804864253371432708308053019780486425337BookABIS_BOOK2002-12-18Dover Publications2002-12-18Dover PublicationsMathematical Logic (Dover Books on Mathematics)266USD$2.66
    US$23.05
    US$1.9 (8%)
    Category: Paperback (2002-12-18)
    Publisher: Dover Publications
    ISBN: 0486425339
    Sales Rank: 533811
    Lowest New Price: $13.87
    Lowest Used Price: $11.70 (28 Used Items)
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    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), Hilbert-type proof theory, and proof theory handled through derived rules.
    The second part supplements the previously discussed material and introduces some of the newer ideas and the more profound results of twentieth-century logical research. Subsequent chapters explore the study of formal number theory, with surveys of the famous incompleteness and undecidability results of Godel, Church, Turing, and others. The emphasis in the final chapter reverts to logic, with examinations of Godel's completeness theorem, Gentzen's theorem, Skolem's paradox and nonstandard models of arithmetic, and other theorems. The author, Stephen Cole Kleene, was Cyrus C. MacDuffee Professor of Mathematics at the University of Wisconsin, Madison. Preface. Bibliography. Theorem and Lemma Numbers: Pages. List of Postulates. Symbols and Notations. Index.

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    1. Introduction to Logic: and to the Methodology of Deductive Sciences (Dover Books on Mathematics)
    2. First-Order Logic (Dover Books on Mathematics)
    3. Introduction to Metamathematics
    4. Number Theory (Dover Books on Mathematics)
    5. Book of Proof
    6. An Introduction to Mathematical Logic (Dover Books on Mathematics)
    7. Introduction to Topology: Third Edition (Dover Books on Mathematics)
    8. Introduction to Graph Theory (Dover Books on Mathematics)
    9. A Book of Abstract Algebra: Second Edition (Dover Books on Mathematics)
    10. A Beginner's Guide to Mathematical Logic (Dover Books on Mathematics) .


    2. Mathematical Logic (Oxford Texts in Logic)
    by Ian Chiswell, Wilfrid Hodges
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    US$71.00Oxford University Press1296599441146611BookABIS_BOOK2007-07-12Oxford University PressOxford University PressMathematical Logic (Oxford Texts in Logic)440USD$4.40
    US$71.00
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    Category: Paperback (2007-07-12)
    Publisher: Oxford University Press
    ISBN: 0199215626
    Sales Rank: 1432577
    Lowest New Price: $50.01
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    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 first-order 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 first-order 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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    Similar Items:
    1. A Friendly Introduction to Mathematical Logic
    2. Propositional and Predicate Calculus: A Model of Argument
    3. An Introduction to Formal Logic
    4. How to Prove It: A Structured Approach, 2nd Edition
    5. Intermediate Logic
    6. Elements of Set Theory
    7. Classic Set Theory: For Guided Independent Study (Chapman & Hall Mathematics)
    8. An Introduction to Non-Classical Logic: From If to Is (Cambridge Introductions to Philosophy)
    9. Friendly Introduction to Mathematical Logic, A
    10. First-Order Logic (Dover Books on Mathematics) .


    3. A Beginner's Guide to Mathematical Logic (Dover Books on Mathematics)
    by Raymond M. Smullyan
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    US$19.95Dover Publications128871913846141BookABIS_BOOK2014-07-16Dover Publications2014-06-18Dover PublicationsA Beginner's Guide to Mathematical Logic (Dover Books on Mathematics)305USD$3.05
    US$18.73
    US$1.22 (6%)
    Category: Paperback (2014-07-16)
    Publisher: Dover Publications
    ISBN: 0486492370
    Sales Rank: 117901
    Lowest New Price: $11.51
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    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.
    Smullyan's accessible narrative provides memorable examples of concepts related to proofs, propositional logic and first-order logic, incompleteness theorems, and incompleteness proofs. Additional topics include undecidability, combinatoric logic, and recursion theory. Suitable for undergraduate and graduate courses, this book will also amuse and enlighten mathematically minded readers. 2014 edition.

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    4. An Introduction to Mathematical Logic (Dover Books on Mathematics)
    by Richard E. Hodel
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    US$29.95Dover Publications15121209201406101BookABIS_BOOK2013-02-20Dover Publications2013-01-24Dover PublicationsAn Introduction to Mathematical Logic (Dover Books on Mathematics)200USD$2.00
    US$20.39
    US$9.56 (32%)
    Category: Paperback (2013-02-20)
    Publisher: Dover Publications
    ISBN: 0486497852
    Sales Rank: 644522
    Lowest New Price: $16.72
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    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 first-order 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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    1. Mathematical Logic (Dover Books on Mathematics)
    2. Introduction to Logic: and to the Methodology of Deductive Sciences (Dover Books on Mathematics)
    3. A Book of Set Theory (Dover Books on Mathematics)
    4. A Book of Abstract Algebra: Second Edition (Dover Books on Mathematics)
    5. Introduction to Topology: Third Edition (Dover Books on Mathematics)
    6. Book of Proof
    7. A Beginner's Guide to Mathematical Logic (Dover Books on Mathematics)
    8. Number Theory (Dover Books on Mathematics)
    9. Linear Algebra Done Right (Undergraduate Texts in Mathematics)
    10. An Introduction to Information Theory: Symbols, Signals and Noise (Dover Books on Mathematics) .


    5. Mathematical Logic, 2nd Edition (Undergraduate Texts in Mathematics)
    by H.-D. Ebbinghaus, J. Flum, Wolfgang Thomas
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    US$79.95Springer1291719291236301BookABIS_BOOK1996-11-15SpringerSpringerMathematical Logic, 2nd Edition (Undergraduate Texts in Mathematics)914USD$9.14
    US$63.96
    US$15.99 (20%)
    Category: Hardcover (1996-11-15)
    Publisher: Springer
    ISBN: 0387942580
    Sales Rank: 1079418
    Lowest New Price: $56.65
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    This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving 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 first-order logic, and the fundamentals of logic programming.

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    1. Real Analysis: Modern Techniques and Their Applications
    2. A Mathematical Introduction to Logic, Second Edition
    3. An Introduction to Mathematical Logic (Dover Books on Mathematics)
    4. Real Analysis for Graduate Students, Second Edition
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    6. A Friendly Introduction to Mathematical Logic
    by Christopher C. Leary
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    US$33.50
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    Category: Paperback (2015-08-10)
    Publisher: Milne Library
    ISBN: 1942341075
    Sales Rank: 807185
    Lowest New Price: $25.90
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    At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary's user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition's treatment of languages, structures, and deductions, leading to rigorous proofs of Gödel's First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises.

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    1. Mathematical Logic (Oxford Texts in Logic)
    2. What is Mathematical Logic? (Dover Books on Mathematics)
    3. Set Theory: A First Course (Cambridge Mathematical Textbooks)
    4. Book of Proof
    5. Propositional and Predicate Calculus: A Model of Argument
    6. First-Order Logic (Dover Books on Mathematics)
    7. Logic, Mathematics, and Computer Science: Modern Foundations with Practical Applications
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    10. A Mathematical Introduction to Logic .


    7. A Course in Mathematical Logic for Mathematicians (Graduate Texts in Mathematics)
    by Yu. I. Manin
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    US$69.95Springer13841209301556401BookABIS_BOOK2009-10-30SpringerSpringerA Course in Mathematical Logic for Mathematicians (Graduate Texts in Mathematics)130USD$1.30
    US$56.09
    US$13.86 (20%)
    Category: Hardcover (2009-10-30)
    Publisher: Springer
    ISBN: 1441906142
    Sales Rank: 1322538
    Lowest New Price: $50.51
    Lowest Used Price: $54.72 (17 Used Items)
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    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 set-theoretic 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 no-nonsense 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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    1. Category Theory (Oxford Logic Guides)
    2. Forcing for Mathematicians
    3. The Oxford Handbook of Philosophy of Mathematics and Logic (Oxford Handbooks)
    4. Model Theory: Third Edition (Dover Books on Mathematics)
    5. Set Theory An Introduction To Independence Proofs (Studies in Logic and the Foundations of Mathematics)
    6. Counterexamples in Probability: Third Edition (Dover Books on Mathematics)
    7. A Mathematical Introduction to Logic, Second Edition
    8. Introduction to Topological Manifolds (Graduate Texts in Mathematics)
    9. Differential Topology (Graduate Texts in Mathematics)
    10. An Introduction to Mathematical Logic (Dover Books on Mathematics) .


    8. Introduction to Logic: and to the Methodology of Deductive Sciences (Dover Books on Mathematics)
    by Alfred Tarski
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    US$14.95
    US$10.66
    US$4.29 (29%)
    Category: Paperback Brand: Tarski, Alfred
    (1995-03-27)
    Publisher: Dover Publications
    ISBN: 048628462X
    Sales Rank: 96697
    Lowest New Price: $8.64
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    First published in Polish in 1936, this classic work was originally written as a popular scientific book — one that would present to the educated lay reader a clear picture of certain powerful trends of thought in modern logic. According to the author, these trends sought to create a unified conceptual apparatus as a common basis for the whole of human knowledge.
    Because these new developments in logical thought tended to perfect and sharpen the deductive method, an indispensable tool in many fields for deriving conclusions from accepted assumptions, the author decided to widen the scope of the work. In subsequent editions he revised the book to make it also a text on which to base an elementary college course in logic and the methodology of deductive sciences. It is this revised edition that is reprinted here.
    Part One deals with elements of logic and the deductive method, including the use of variables, sentential calculus, theory of identity, theory of classes, theory of relations and the deductive method. The Second Part covers applications of logic and methodology in constructing mathematical theories, including laws of order for numbers, laws of addition and subtraction, methodological considerations on the constructed theory, foundations of arithmetic of real numbers, and more. The author has provided numerous exercises to help students assimilate the material, which not only provides a stimulating and thought-provoking introduction to the fundamentals of logical thought, but is the perfect adjunct to courses in logic and the foundation of mathematics.

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    Similar Items:
    1. Mathematical Logic (Dover Books on Mathematics)
    2. First-Order Logic (Dover Books on Mathematics)
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    5. An Investigation of the Laws of Thought
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    9. A Mathematical Introduction to Logic, Second Edition
    by Herbert B. Enderton
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    US$113.00Academic Press13171009301656201BookABIS_BOOK2001-01-05Academic PressAcademic PressA Mathematical Introduction to Logic, Second Edition700USD$7.00
    US$101.70
    US$11.3 (10%)
    Category: Hardcover Brand: Tarski, Alfred
    (2001-01-05)
    Publisher: Academic Press
    ISBN: 0122384520
    Sales Rank: 695099
    Lowest New Price: $48.68
    Lowest Used Price: $28.95 (40 Used Items)
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    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

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    10. My Best Mathematical and Logic Puzzles (Dover Recreational Math)
    by Martin Gardner
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    US$5.95
    US$4.95
    US$1 (17%)
    Category: Paperback Brand: Dover Publications
    (1994-11-01)
    Publisher: Dover Publications
    ISBN: 0486281523
    Sales Rank: 9265
    Lowest New Price: $1.84
    Lowest Used Price: $0.95 (70 Used Items)
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    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.
    The present volume contains a rich selection of 70 of the best of these brain teasers, in some cases including references to new developments related to the puzzle. Now enthusiasts can challenge their solving skills and rattle their egos with such stimulating mind-benders as The Returning Explorer, The Mutilated Chessboard, Scrambled Box Tops, The Fork in the Road, Bronx vs. Brooklyn, Touching Cigarettes, and 64 other problems involving logic and basic math. Solutions are included.

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    • Dover Publications

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