Mathematical Logic - H.-D. Ebbinghaus
KORTE INHOUD
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 Goedel's 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...
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Original boards, illustrated with numerous equations, 8vo. Undergraduate Texts in Mathematics.; Name in pen on title page. [Auteur: Ebbinghaus, H.- D. & J. Flum & W. Thomas] [Pagina's: 289] [Taal: en] [Uitgever: New York : Springer-Verlag] [Jaar: 1994] [Titel: Mathematical Logic - 2nd Edition]
