Practical foundations of mathematics

Paul Taylor

Practical Foundations collects the methods of construction of the objects of twentieth-century mathematics. Although it is mainly concerned with a framework essentially equivalent to intuitionistic Zermelo-Fraenkel logic, the book looks forward to more subtle bases in categorical type theory and the machine representation of mathematics. Each idea is illustrated by wide-ranging examples, and followed critically along its natural path, transcending disciplinary boundaries between universal algebra, type theory, category theory, set theory, sheaf theory, topology and programming. Students and teachers of computing, mathematics and philosophy will find this book both readable and of lasting value as a reference work.

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[目次]

  • 1. First order reasoning
  • 2. Types and induction
  • 3. Posets and lattices
  • 4. Cartesian closed categories
  • 5. Limits and colimits
  • 6. Structural recursion
  • 7. Adjunctions
  • 8. Algebra with dependent types
  • 9. The quantifiers.

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この本の情報

書名 Practical foundations of mathematics
著作者等 Taylor, Paul
シリーズ名 Cambridge studies in advanced mathematics
出版元 Cambridge University Press
刊行年月 1999
ページ数 xi, 572 p.
大きさ 24 cm
ISBN 0521631076
NCID BA40980043
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言語 英語
出版国 イギリス
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