Anbieter: BooksRun, Philadelphia, PA, USA
Hardcover. Zustand: Very Good. 2nd. It's a well-cared-for item that has seen limited use. The item may show minor signs of wear. All the text is legible, with all pages included. It may have slight markings and/or highlighting.
Anbieter: Labyrinth Books, Princeton, NJ, USA
Zustand: New.
Sprache: Englisch
Verlag: New York : Springer-Verlag, 1994
ISBN 10: 0387942580 ISBN 13: 9780387942582
Anbieter: Klondyke, Almere, Niederlande
Zustand: Good. Original boards, illustrated with numerous equations, 8vo. Undergraduate Texts in Mathematics.; Name in pen on title page.
Anbieter: AproposBooks&Comics, London, Vereinigtes Königreich
EUR 41,67
Anzahl: 1 verfügbar
In den WarenkorbHardcover. Zustand: Fine. 2nd Edition.
Anbieter: Ria Christie Collections, Uxbridge, Vereinigtes Königreich
EUR 71,55
Anzahl: Mehr als 20 verfügbar
In den WarenkorbZustand: New. In.
Anbieter: AHA-BUCH GmbH, Einbeck, Deutschland
Buch. Zustand: Neu. 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.