Mathematical Logic by H.-D. Ebbinghaus (English) Hardcover Book

The Nile on eBay   Mathematical Logic by H.-D. Ebbinghaus, J. Flum, Wolfgang Thomas

Our first goal is Godel's completeness theorem, which shows that the con­ sequence relation coincides with formal provability: By means of a calcu­ lus consisting of simple formal inference rules, one can obtain all conse­ quences of a given axiom system (and in particular, imitate all mathemat­ ical proofs).

FORMATHardcover LANGUAGEEnglish CONDITIONBrand New Publisher Description

What is a mathematical proof? How can proofs be justified? Are there limitations to provability? To what extent can machines carry out mathe­ matical proofs? Only in this century has there been success in obtaining substantial and satisfactory answers. The present book contains a systematic discussion of these results. The investigations are centered around first-order logic. Our first goal is Godel's completeness theorem, which shows that the con­ sequence relation coincides with formal provability: By means of a calcu­ lus consisting of simple formal inference rules, one can obtain all conse­ quences of a given axiom system (and in particular, imitate all mathemat­ ical proofs). A short digression into model theory will help us to analyze the expres­ sive power of the first-order language, and it will turn out that there are certain deficiencies. For example, the first-order language does not allow the formulation of an adequate axiom system for arithmetic or analysis. On the other hand, this difficulty can be overcome--even in the framework of first-order logic-by developing mathematics in set-theoretic terms. We explain the prerequisites from set theory necessary for this purpose and then treat the subtle relation between logic and set theory in a thorough manner.

Notes

This junior/senior level text starts with a thorough treatment of first-order logic and its role in the foundations of mathematics. It covers several advanced topics, not commonly treated in introductory texts, such as Trachtenbrot's undecidability theorem, Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.

Table of Contents

A.- I Introduction.- II Syntax of First-Order Languages.- III Semantics of First-Order Languages.- IV A Sequent Calculus.- V The Completeness Theorem.- VI The Löwenheim-Skolem and the Compactness Theorem.- VII The Scope of First-Order Logic.- VIII Syntactic Interpretations and Normal Forms.- B.- IX Extensions of First-Order Logic.- X Limitations of the Formal Method.- XI Free Models and Logic Programming.- XII An Algebraic Characterization of Elementary Equivalence.- XIII Lindström's Theorems.- References.- Symbol Index.

Review

"…the book remains my text of choice for this type of material, and I highly recommend it to anyone teaching a first logic course at this level." – Journal of Symbolic Logic

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Corrected second printing

Long Description

What is a mathematical proof? How can proofs be justified? Are there limitations to provability? To what extent can machines carry out mathe

Review Text

"...the book remains my text of choice for this type of material, and I highly recommend it to anyone teaching a first logic course at this level." - Journal of Symbolic Logic

Review Quote

"...the book remains my text of choice for this type of material, and I highly recommend it to anyone teaching a first logic course at this level." - Journal of Symbolic Logic

Description for Sales People

This junior/senior level text starts with a thorough treatment of first-order logic and its role in the foundations of mathematics. It covers several advanced topics, not commonly treated in introductory texts, such as Trachtenbrot's undecidability theorem, Fra

Details ISBN0387942580 Series Undergraduate Texts in Mathematics Language English Edition 2nd ISBN-10 0387942580 ISBN-13 9780387942582 Media Book Format Hardcover DEWEY 511.3 Imprint Springer-Verlag New York Inc. Place of Publication New York, NY Country of Publication United States Short Title MATHEMATICAL LOGIC 1994 CORR 2 Pages 291 Replaces 9780387908953 DOI 10.1007/b18411;10.1007/978-1-4757-2355-7 UK Release Date 1996-11-15 AU Release Date 1996-11-15 NZ Release Date 1996-11-15 Author Wolfgang Thomas Publisher Springer-Verlag New York Inc. Alternative 9781475723571 Illustrations X, 291 p. Audience Undergraduate Edition Description 2nd ed. 1994 Year 1994 Publication Date 1994-06-10 US Release Date 1994-06-10 We've got this

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