Undergraduate Texts in Mathematics

Mathematical Logic

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

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About this Textbook

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.

Table of contents (13 chapters)

Table of contents (13 chapters)

Buy this book

eBook $59.99
price for USA in USD
  • ISBN 978-1-4757-2355-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.95
price for USA in USD
  • ISBN 978-0-387-94258-2
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions & severe weather in the US may cause delays
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $79.95
price for USA in USD
  • ISBN 978-1-4757-2357-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions & severe weather in the US may cause delays
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Mathematical Logic
Authors
Series Title
Undergraduate Texts in Mathematics
Copyright
1994
Publisher
Springer-Verlag New York
Copyright Holder
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
Softcover ISBN
978-1-4757-2357-1
Series ISSN
0172-6056
Edition Number
2
Number of Pages
X, 291
Topics