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Algebraic Set Theory
André JoyalIeke Moerdijk
出版Cambridge University Press, 1995-09-14
主題Mathematics / Algebra / GeneralMathematics / LogicMathematics / Set TheoryScience / General
ISBN05215583019780521558303
URLhttp://books.google.com.hk/books?id=E0Xhn32xzZAC&hl=&source=gbs_api
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註釋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 these 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 realizability 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 a background in categorical logic.