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.
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