Algebraic Set Theory
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.
- Electronic book text
- 11 May 2012
- CAMBRIDGE UNIVERSITY PRESS
- Cambridge University Press (Virtual Publishing)
- Cambridge, United Kingdom
"Graduate students and researchers in mathematical logic, category theory and computer science should find this book of great interest." Ioan Tofan, Mathematical Reviews
Table of contents
1. Axiomatic theory of small maps; 2. Zermelo-Fraenkel algebras; 3. Existence theorems; 4. Examples.