Mathematical Logic - Couverture rigide

Ebbinghaus, H-. D.; Etc.; Flum, J.; Thomas, W.

Couverture rigide

ISBN 10 : 3540942580 ISBN 13 : 9783540942580

Editeur : Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1994

Synopsis

This junior/senior level text is devoted to a study of first-order logic and its role in the foundations of mathematics: What is a proof? How can a proof be justified? To what extent can a proof be made a purely mechanical procedure? How much faith can we have in a proof that is so complex that no one can follow it through in a lifetime? The first substantial answers to these questions have only been obtained in this century. The most striking results are contained in Goedells work: First, it is possible to give a simple set of rules that suffice to carry out all mathematical proofs; but, second, these rules are necessarily incomplete - it is impossible, for example, to prove all true statements of arithmetic. The book begins with an introduction to first-order logic, Goedel's theorem, and model theory. A second part covers extensions of first-order logic and limitations of the formal methods. The book covers several advanced topics, not commonly treated in introductory texts, such as Trachtenbrot's undecidability theorem. Fraisse's elementary equivalence, and Lindstroem's theorem on the maximality of first-order logic.

Détails de l'édition

• Éditeur: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Date d'édition: 1994
• Langue: anglais
• ISBN 10: 3540942580
• ISBN 13: 9783540942580
• Reliure: Relié
• Nombre de pages: 299
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible