A Beginner's Guide to Mathematical Logic

Author: Raymond M. Smullyan

Publisher: Courier Corporation

ISBN: 0486492370

Category: Mathematics

Page: 288

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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. Dover (2014) original publication. See every Dover book in print at www.doverpublications.com

An Introduction to Mathematical Logic

Author: Richard E. Hodel

Publisher: Courier Corporation

ISBN: 0486497852

Category: Mathematics

Page: 491

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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.

Introduction to Elementary Mathematical Logic

Author: Abram Aronovich Stolyar

Publisher: Courier Corporation

ISBN: 0486645614

Category: Mathematics

Page: 209

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This lucid, non-intimidating presentation by a Russian scholar explores propositional logic, propositional calculus, and predicate logic. Topics include computer science and systems analysis, linguistics, and problems in the foundations of mathematics. Accessible to high school students, it also constitutes a valuable review of fundamentals for professionals. 1970 edition.

An Introduction to Symbolic Logic

Author: Langer

Publisher: Courier Corporation

ISBN: 9780486601649

Category: Mathematics

Page: 384

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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.

First Order Mathematical Logic

Author: Angelo Margaris

Publisher: Courier Corporation

ISBN: 9780486662695

Category: Mathematics

Page: 211

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"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

Introduction to Logic

Author: Patrick Suppes

Publisher: Courier Corporation

ISBN: 9780486406879

Category: Mathematics

Page: 312

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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.

Kurt Gödel

Jahrhundertmathematiker und großer Entdecker

Author: Rebecca Goldstein

Publisher: N.A

ISBN: 9783492249607

Category:

Page: 312

View: 1912

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Foundations of Mathematical Logic

Author: Haskell Brooks Curry

Publisher: Courier Corporation

ISBN: 9780486634623

Category: Mathematics

Page: 408

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Written by a pioneer of mathematical logic, this comprehensive graduate-level text explores the constructive theory of first-order predicate calculus. It covers formal methods — including algorithms and epitheory — and offers a brief treatment of Markov's approach to algorithms. It also explains elementary facts about lattices and similar algebraic systems. 1963 edition.

First Course in Mathematical Logic

Author: Patrick Suppes,Shirley Hill

Publisher: Courier Corporation

ISBN: 0486150941

Category: Mathematics

Page: 288

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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.

Grundzüge der Mengenlehre

Author: Felix Hausdorff

Publisher: American Mathematical Soc.

ISBN: 9780828400619

Category: Mathematics

Page: 476

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This reprint of the original 1914 edition of this famous work contains many topics that had to be omitted from later editions, notably, Symmetric Sets, Principle of Duality, most of the ``Algebra'' of Sets, Partially Ordered Sets, Arbitrary Sets of Complexes, Normal Types, Initial and Final Ordering, Complexes of Real Numbers, General Topological Spaces, Euclidean Spaces, the Special Methods Applicable in the Euclidean Plane, Jordan's Separation Theorem, the Theory of Content and Measure, the Theory of the Lebesgue Integral. The text is in German.

A Profile of Mathematical Logic

Author: Howard DeLong

Publisher: Courier Corporation

ISBN: 0486139158

Category: Mathematics

Page: 320

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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.

Philosophical Introduction to Set Theory

Author: Stephen Pollard

Publisher: Courier Dover Publications

ISBN: 0486805824

Category: Mathematics

Page: 192

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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.

Set Theory and Logic

Author: Robert R. Stoll

Publisher: Courier Corporation

ISBN: 0486139646

Category: Mathematics

Page: 512

View: 972

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Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.

Introduction to Mathematical Philosophy

Author: Bertrand Russell

Publisher: Courier Corporation

ISBN: 9780486277240

Category: Mathematics

Page: 208

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In the words of Bertrand Russell, "Because language is misleading, as well as because it is diffuse and inexact when applied to logic (for which it was never intended), logical symbolism is absolutely necessary to any exact or thorough treatment of mathematical philosophy." That assertion underlies this book, a seminal work in the field for more than 70 years. In it, Russell offers a nontechnical, undogmatic account of his philosophical criticism as it relates to arithmetic and logic. Rather than an exhaustive treatment, however, the influential philosopher and mathematician focuses on certain issues of mathematical logic that, to his mind, invalidated much traditional and contemporary philosophy. In dealing with such topics as number, order, relations, limits and continuity, propositional functions, descriptions, and classes, Russell writes in a clear, accessible manner, requiring neither a knowledge of mathematics nor an aptitude for mathematical symbolism. The result is a thought-provoking excursion into the fascinating realm where mathematics and philosophy meet — a philosophical classic that will be welcomed by any thinking person interested in this crucial area of modern thought.

Introduction to Logic and to the Methodology of Deductive Sciences

Author: Alfred Tarski

Publisher: Courier Corporation

ISBN: 048628462X

Category: Mathematics

Page: 239

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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 layman a clear picture of certain powerful trends of thought in modern logic.