Verwandte Artikel zu Mathematical Logic (Undergraduate Texts in Mathematics)

Mathematical Logic (Undergraduate Texts in Mathematics) - Hardcover

Buch 121 von 170: Undergraduate Texts in Mathematics

Ebbinghaus, H.-D.; Flum, J.; Thomas, Wolfgang

 
9780387942582: Mathematical Logic (Undergraduate Texts in Mathematics)
Hardcover
ISBN 10: 0387942580 ISBN 13: 9780387942582
Verlag: Springer, 1994

Inhaltsangabe

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.

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The book 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 Fraisse's characterization of elementary equivalence, Lindstrom's theorem on the maximality of first-order logic, and the fundamentals of logic programming.

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Verlag
Springer
Erscheinungsdatum
1994
Sprache
Englisch
ISBN 10 
0387942580
ISBN 13 
9780387942582
Einband
Gebundene Ausgabe
Auflage
2
Anzahl der Seiten
301
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