Mathematical Logic

Beschreibung

Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 308 pp. Englisch.

Bestandsnummer des Verkäufers 9780387942582

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Bibliografische Details

Titel

Mathematical Logic

Verlag

Springer New York, Springer US Jun 1994

Erscheinungsjahr

1994

Sprache

Englisch

ISBN-10

0387942580

ISBN-13

9780387942582

Einband

Buch

Auflage

2. Auflage

Zustand

Neu

Abmessungen

241B x 160 H x 22 T Millimeter Breite: 241 mm, Höhe: 160 mm, Tiefe: 22 mm

Gewicht

629 Gramm

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