*^Mathematical Logic
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Book Details
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Publisher: Dover
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Author: Stephen Cole Kleene
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Language: English
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ISBN: 9780486425337
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Pages: 416
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Cover: Paperback
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Release Date: 18-12-2002
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Dimensions: 8.5 x 5.6 x 1.3 inches
About The Book
Mathematical Logic by Stephen Cole Kleene is an invaluable text for undergraduate students venturing into the world of mathematical logic, especially those with no prior classroom instruction on the subject. Written by one of the greatest authorities on mathematical logic, this evenhanded and multipart text provides a thorough introduction to the subject, offering a balance of elementary yet comprehensive instruction.
The book is divided into two parts:
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Part I focuses on the mathematical logic of first-order logic, starting with foundational techniques. Students are introduced to model theory (truth tables), Hilbert-type proof theory, and proof theory using derived rules. This structured approach ensures a clear understanding of the core elements of mathematical logic.
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Part II builds on the material from Part I, delving into newer concepts and significant twentieth-century advancements in logical research. This section covers formal number theory, as well as important results such as Gödel’s incompleteness and undecidability theorems, and contributions from key figures like Church and Turing.
The final chapters of the book return to logic, exploring some of the most profound theorems in the field, including Gödel's completeness theorem, Gentzen's theorem, Skolem's paradox, and nonstandard models of arithmetic. These topics offer a deep dive into the foundational aspects of logic that have shaped modern mathematical theory.
An unabridged republication of the edition published by John Wiley & Sons, Inc. in 1967, this edition includes a preface, bibliography, theorem and lemma numbers, a list of postulates, symbols and notations, and an index, making it a complete and invaluable resource for anyone studying mathematical logic.