Hardback. Very Good. ISBN 0387942580 9780387942582 [GB]

Springer, Date: 1994-06-10. 2nd. Hardcover. Very Good. Ships quickly. Almost like new. Unmarked. No labels. No creased pages. Minimal shelf/reading wear. Orphans Treasure Box sells books to raise money for orphans and vulnerable kids. 1994. Springer ISBN 0387942580 9780387942582 [US]

This book is in very good condition and ready for quick shipment ISBN 0387942580 9780387942582 [US]

ISBN10: 0387942580, ISBN13: 9780387942582, [publisher: Springer New York] Hardcover Druck auf Anfrage Neuware - Printed after ordering - 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.
[Einbeck, Germany] [Publication Year: ...
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ISBN10: 0387942580, ISBN13: 9780387942582, [publisher: Springer New York] Hardcover Druck auf Anfrage Neuware - Printed after ordering - 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.
[Einbeck, Germany] [Publication Year: ...
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Springer, Date: 1996-11-15. Hardcover. Good. Textbook, May Have Highlights, Notes and/or Underlining, BOOK ONLY-NO ACCESS CODE, NO CD, Ships with Emailed Tracking 1996. Springer ISBN 0387942580 9780387942582 [US]