Mathematical Logic

by Ebbinghaus, Heinz-Dieter

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Title Statements

Full title :Mathematical Logic / by H.-D. Ebbinghaus, J. Flum, Wolfgang Thomas.

Summary

"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." -- Prové de l'editor.

Edition Statements

Publication Date:1994
Edition:2nd ed. 1994

Publication Statements

Publisher(s):Springer New York
Place of Publication:New York, NY
Language:eng
Publication Date:1994

The Physical Object

Description:1 recurs en línia (1 recurs en línia (X, 291 pàgines)).

Edition Identifiers

ISBN:9781475723557, 1475723555
DOI:10.1007/978-1-4757-2355-7
oclc:on1251796188
LC Classification:P2E

Conté: 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.