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Mathematical Logic

Mathematical Logic


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About the Book

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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Product Details
  • ISBN-13: 9780387942582
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Depth: 25
  • Height: 239 mm
  • No of Pages: 291
  • Series Title: Undergraduate Texts in Mathematics
  • Weight: 639 gr
  • ISBN-10: 0387942580
  • Publisher Date: 15 Nov 1996
  • Binding: Hardback
  • Edition: 2nd ed. 1994. Corr. 2nd printing 1996
  • Language: English
  • Returnable: N
  • Spine Width: 25 mm
  • Width: 163 mm


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