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Mathematical Logic - 2nd Edition

Door H.- D. Ebbinghaus e.a.

Categorie
Algemeen wetenschap
Boeknummer
#343200-ZA30
Titel
Mathematical Logic - 2nd Edition
Auteur
Ebbinghaus, H.- D. & J. Flum & W. Thomas
Boektype
Gebonden
Uitgeverij
New York : Springer-Verlag
Jaar van uitgave
1994
ISBN10
0387942580
ISBN13
9780387942582
Taal
Engels
Beschrijving
Original boards, illustrated with numerous equations, 8vo. Undergraduate Texts in Mathematics.
Samenvatting
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... (Lees verder) 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.
Pagina's
289
Conditie
Goed — Name in pen on title page.
Prijs
€ 30,00

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