Undergraduate Texts in Mathematics

Mathematical Logic

Autoren: Ebbinghaus, H.-D., Flum, J., Thomas, Wolfgang

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  • ISBN 978-1-4757-2355-7
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Über dieses Lehrbuch

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.

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“…the book remains my text of choice for this type of material, and I highly recommend it to anyone teaching a first logic course at this level.” – Journal of Symbolic Logic


Inhaltsverzeichnis (13 Kapitel)

Inhaltsverzeichnis (13 Kapitel)

Dieses Buch kaufen

eBook 49,99 €
Preis für Deutschland (Brutto)
  • ISBN 978-1-4757-2355-7
  • Versehen mit digitalem Wasserzeichen, DRM-frei
  • Erhältliche Formate: PDF
  • eBooks sind auf allen Endgeräten nutzbar
  • Sofortiger eBook Download nach Kauf
Hardcover 64,15 €
Preis für Deutschland (Brutto)
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Bibliografische Information

Bibliographic Information
Buchtitel
Mathematical Logic
Autoren
Titel der Buchreihe
Undergraduate Texts in Mathematics
Copyright
1994
Verlag
Springer-Verlag New York
Copyright Inhaber
Springer Science+Business Media New York
eBook ISBN
978-1-4757-2355-7
DOI
10.1007/978-1-4757-2355-7
Hardcover ISBN
978-0-387-94258-2
Buchreihen ISSN
0172-6056
Auflage
2
Seitenzahl
X, 291
Themen