Algebraic Set Theory [Paperback]

This book offers a new, algebraic, approach to set theory.Offering a new algebraic approach to set theory, this text introduces a particular kind of algebra, the Zermelo-Fraenkel algebras, which arise from the familiar axioms of Zermelo-Fraenkel set theory. Furthermore, it explicitly constructs such algebras using the theory of bisimulations.Offering a new algebraic approach to set theory, this text introduces a particular kind of algebra, the Zermelo-Fraenkel algebras, which arise from the familiar axioms of Zermelo-Fraenkel set theory. Furthermore, it explicitly constructs such algebras using the theory of bisimulations.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.1. Axiomatic theory of small maps; 2. Zermelo-Fraenkel algebras; 3. Existence theorems; 4. Examples. Graduate students and researchers in mathematical logic, category theory and computer science should find this book of great interest. Ioan Tofan, Mathematical Reviews