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  3. Algebraic Set Theory
  • Cited by 51
Publisher:
Cambridge University Press
Online publication date:
August 2010
Print publication year:
1995
Online ISBN:
9780511752483
DOI:
https://doi.org/10.1017/CBO9780511752483
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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