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Set Theory, Logic and their Limitations

Set Theory, Logic and their Limitations


  • Date Published: May 1996
  • availability: Available
  • format: Paperback
  • isbn: 9780521479981

$ 57.99

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About the Authors
  • This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations. A rigorous axiomatic presentation of Zermelo-Fraenkel set theory is given, demonstrating how the basic concepts of mathematics have apparently been reduced to set theory. This is followed by a presentation of propositional and first-order logic. Concepts and results of recursion theory are explained in intuitive terms, and the author proves and explains the limitative results of Skolem, Tarski, Church and Gödel (the celebrated incompleteness theorems). For students of mathematics or philosophy this book provides an excellent introduction to logic and set theory.

    • Course tested at the University of London
    • Suitable for courses in both pure mathematics and philosophy (and there are several joint mathematics/philosophy courses)
    • Author well known in the field, wrote THE book years ago (see above)
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    Reviews & endorsements

    ' … written by an excellent mathematician … I very much like the way the author explains things.' European Mathematical Society

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    Product details

    • Date Published: May 1996
    • format: Paperback
    • isbn: 9780521479981
    • length: 300 pages
    • dimensions: 228 x 153 x 15 mm
    • weight: 0.51kg
    • availability: Available
  • Table of Contents

    Mathematical induction
    1. Sets and classes
    2. Relations and functions
    3. Cardinals
    4. Ordinals
    5. The axiom of choice
    6. Finite cardinals and alephs
    7. Propositional logic
    8. First order logic
    9. Facts from recursion theory
    10. Limitative results
    Appendix: Skolem's paradox.

  • Author

    Moshe Machover, King's College London

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