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  3. Algebraic Set Theory
  • Cited by 53
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    • Publisher:
      Cambridge University Press
      Publication date:
      August 2010
      September 1995
      ISBN:
      9780511752483
      9780521558303
      DOI:
      https://doi.org/10.1017/CBO9780511752483
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.21kg, 132 Pages
      • Subjects:
      Mathematics (general), Mathematics, Algorithmics, Complexity, Computer Algebra, Computational Geometry, Logic, Categories and Sets, Computer Science
      Series:
      London Mathematical Society Lecture Note Series (220)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Algorithmics, Complexity, Computer Algebra, Computational Geometry, Logic, Categories and Sets, Computer Science
    Series:
    London Mathematical Society Lecture Note Series (220)
    Information

    Book description

    This book offers a new, algebraic, approach to set theory. The authors introduce a particular kind of algebra, the Zermelo-Fraenkel algebras, which arise from the familiar axioms of Zermelo-Fraenkel set theory. Furthermore the authors explicitly construct such algebras using the theory of bisimulations. Their approach is completely constructive, and contains both intuitionistic set theory and topos theory. In particular it provides a uniform description of various constructions of the cumulative hierarchy of sets in forcing models, sheaf models and realisability models. Graduate students and researchers in mathematical logic, category theory and computer science should find this book of great interest, and it should be accessible to anyone with some background in categorical logic.

    Reviews

    "Graduate students and researchers in mathematical logic, category theory and computer science should find this book of great interest." Ioan Tofan, Mathematical Reviews

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