An Introduction to Mathematical Logic

Author: Richard E. Hodel

Publisher: Courier Corporation

ISBN: 0486497852

Category: Mathematics

Page: 491

View: 969

This comprehensive overview ofmathematical logic is designedprimarily for advanced undergraduatesand graduate studentsof mathematics. The treatmentalso contains much of interest toadvanced students in computerscience and philosophy. Topics include propositional logic;first-order languages and logic; incompleteness, undecidability,and indefinability; recursive functions; computability;and Hilbert’s Tenth Problem.Reprint of the PWS Publishing Company, Boston, 1995edition.
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Introduction to Logic

Author: Patrick Suppes

Publisher: Courier Corporation

ISBN: 0486138054

Category: Mathematics

Page: 336

View: 3436

Part I of this coherent, well-organized text deals with formal principles of inference and definition. Part II explores elementary intuitive set theory, with separate chapters on sets, relations, and functions. Ideal for undergraduates.
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Introduction to Logic and to the Methodology of Deductive Sciences

Author: Alfred Tarski

Publisher: Courier Corporation

ISBN: 048628462X

Category: Mathematics

Page: 239

View: 973

First published in Polish in 1936, this classic work was originally written as a popular scientific book - one that would present to the educated layman a clear picture of certain powerful trends of thought in modern logic.
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Mathematical Logic

Author: Stephen Cole Kleene

Publisher: Courier Corporation

ISBN: 0486317072

Category: Mathematics

Page: 416

View: 4082

Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more.
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Mathematics and Logic

Author: Mark Kac,Stanislaw M. Ulam

Publisher: Courier Corporation

ISBN: 0486670856

Category: Philosophy

Page: 170

View: 8574

Fascinating study of the origin and nature of mathematical thought, including relation of mathematics and science, 20th-century developments, impact of computers, and more.Includes 34 illustrations. 1968 edition."
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First-order Logic

Author: Raymond M. Smullyan

Publisher: Courier Corporation

ISBN: 9780486683706

Category: Mathematics

Page: 158

View: 9955

Considered the best book in the field, this completely self-contained study is both an introduction to quantification theory and an exposition of new results and techniques in "analytic" or "cut free" methods. The focus in on the tableau point of view. Topics include trees, tableau method for propositional logic, Gentzen systems, more. Includes 144 illustrations.
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A Profile of Mathematical Logic

Author: Howard DeLong

Publisher: Courier Corporation

ISBN: 0486139158

Category: Mathematics

Page: 320

View: 6052

This introduction to mathematical logic explores philosophical issues and Gödel's Theorem. Its widespread influence extends to the author of Gödel, Escher, Bach, whose Pulitzer Prize–winning book was inspired by this work.
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Introduction to Mathematical Logic, Sixth Edition

Author: Elliott Mendelson

Publisher: CRC Press

ISBN: 1482237784

Category: Mathematics

Page: 513

View: 964

The new edition of this classic textbook, Introduction to Mathematical Logic, Sixth 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. The sixth edition incorporates recent work on Gödel’s second incompleteness theorem as well as restoring an appendix on consistency proofs for first-order arithmetic. This appendix last appeared in the first edition. It is offered in the new edition for historical considerations. The text also offers historical perspectives and many new exercises of varying difficulty, which motivate and lead students to an in-depth, practical understanding of the material.
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A Beginner's Guide to Mathematical Logic

Author: Raymond M. Smullyan

Publisher: Courier Corporation

ISBN: 0486492370

Category: Mathematics

Page: 288

View: 3645

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. Dover (2014) original publication. See every Dover book in print at www.doverpublications.com
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An Introduction to Symbolic Logic

Author: Langer

Publisher: Courier Corporation

ISBN: 9780486601649

Category: Mathematics

Page: 384

View: 3378

Famous classic has introduced countless readers to symbolic logic with its thorough and precise exposition. Starts with simple symbols and conventions and concludes with the Boole-Schroeder and Russell-Whitehead systems. No special knowledge of mathematics necessary. "One of the clearest and simplest introductions to a subject which is very much alive." — Mathematics Gazette.
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Introduction to Symbolic Logic and Its Applications

Author: Rudolf Carnap

Publisher: Courier Corporation

ISBN: 048614349X

Category: Mathematics

Page: 272

View: 8252

Clear, comprehensive, and rigorous treatment develops the subject from elementary concepts to the construction and analysis of relatively complex logical languages. Hundreds of problems, examples, and exercises. 1958 edition.
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A Friendly Introduction to Mathematical Logic

Author: Christopher C. Leary,Lars Kristiansen

Publisher: Lulu.com

ISBN: 1942341075

Category:

Page: 380

View: 6666

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 Godel'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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First Course in Mathematical Logic

Author: Patrick Suppes,Shirley Hill

Publisher: Courier Corporation

ISBN: 0486150941

Category: Mathematics

Page: 288

View: 7296

Rigorous introduction is simple enough in presentation and context for wide range of students. Symbolizing sentences; logical inference; truth and validity; truth tables; terms, predicates, universal quantifiers; universal specification and laws of identity; more.
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First Order Mathematical Logic

Author: Angelo Margaris

Publisher: Courier Corporation

ISBN: 9780486662695

Category: Mathematics

Page: 211

View: 6333

"Attractive and well-written introduction." — Journal of Symbolic Logic The logic that mathematicians use to prove their theorems is itself a part of mathematics, in the same way that algebra, analysis, and geometry are parts of mathematics. This attractive and well-written introduction to mathematical logic is aimed primarily at undergraduates with some background in college-level mathematics; however, little or no acquaintance with abstract mathematics is needed. Divided into three chapters, the book begins with a brief encounter of naïve set theory and logic for the beginner, and proceeds to set forth in elementary and intuitive form the themes developed formally and in detail later. In Chapter Two, the predicate calculus is developed as a formal axiomatic theory. The statement calculus, presented as a part of the predicate calculus, is treated in detail from the axiom schemes through the deduction theorem to the completeness theorem. Then the full predicate calculus is taken up again, and a smooth-running technique for proving theorem schemes is developed and exploited. Chapter Three is devoted to first-order theories, i.e., mathematical theories for which the predicate calculus serves as a base. Axioms and short developments are given for number theory and a few algebraic theories. Then the metamathematical notions of consistency, completeness, independence, categoricity, and decidability are discussed, The predicate calculus is proved to be complete. The book concludes with an outline of Godel's incompleteness theorem. Ideal for a one-semester course, this concise text offers more detail and mathematically relevant examples than those available in elementary books on logic. Carefully chosen exercises, with selected answers, help students test their grasp of the material. For any student of mathematics, logic, or the interrelationship of the two, this book represents a thought-provoking introduction to the logical underpinnings of mathematical theory. "An excellent text." — Mathematical Reviews
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Introduction to the Foundations of Mathematics

Second Edition

Author: Raymond L. Wilder

Publisher: Courier Corporation

ISBN: 0486276201

Category: Mathematics

Page: 352

View: 6615

Classic undergraduate text acquaints students with fundamental concepts and methods of mathematics. Topics include axiomatic method, set theory, infinite sets, groups, intuitionism, formal systems, mathematical logic, and much more. 1965 second edition.
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An Introduction to Formal Logic

Author: Peter Smith

Publisher: Cambridge University Press

ISBN: 9780521008044

Category: Mathematics

Page: 357

View: 3849

Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic.
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Topoi

The Categorial Analysis of Logic

Author: R. Goldblatt

Publisher: Elsevier

ISBN: 148329921X

Category: Mathematics

Page: 565

View: 4810

The first of its kind, this book presents a widely accessible exposition of topos theory, aimed at the philosopher-logician as well as the mathematician. It is suitable for individual study or use in class at the graduate level (it includes 500 exercises). It begins with a fully motivated introduction to category theory itself, moving always from the particular example to the abstract concept. It then introduces the notion of elementary topos, with a wide range of examples and goes on to develop its theory in depth, and to elicit in detail its relationship to Kripke's intuitionistic semantics, models of classical set theory and the conceptual framework of sheaf theory (``localization'' of truth). Of particular interest is a Dedekind-cuts style construction of number systems in topoi, leading to a model of the intuitionistic continuum in which a ``Dedekind-real'' becomes represented as a ``continuously-variable classical real number''. The second edition contains a new chapter, entitled Logical Geometry, which introduces the reader to the theory of geometric morphisms of Grothendieck topoi, and its model-theoretic rendering by Makkai and Reyes. The aim of this chapter is to explain why Deligne's theorem about the existence of points of coherent topoi is equivalent to the classical Completeness theorem for ``geometric'' first-order formulae.
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Philosophical Introduction to Set Theory

Author: Stephen Pollard

Publisher: Courier Dover Publications

ISBN: 0486805824

Category: Mathematics

Page: 192

View: 4381

This unique approach maintains that set theory is the primary mechanism for ideological and theoretical unification in modern mathematics, and its technically informed discussion covers a variety of philosophical issues. 1990 edition.
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