Bulletin of Symbolic Logic 14 (3):281-298 (2008)
This brief article is intended to introduce the reader to the field of algebraic set theory, in which models of set theory of a new and fascinating kind are determined algebraically. The method is quite robust, applying to various classical, intuitionistic, and constructive set theories. Under this scheme some familiar set theoretic properties are related to algebraic ones, while others result from logical constraints. Conventional elementary set theories are complete with respect to algebraic models, which arise in a variety of ways, including topologically, type-theoretically, and through variation. Many previous results from topos theory involving realizability, permutation, and sheaf models of set theory are subsumed, and the prospects for further such unification seem bright.
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Citations of this work BETA
Understanding the Infinite II: Coalgebra.David Corfield - 2011 - Studies in History and Philosophy of Science Part A 42 (4):571-579.
Categorical Foundations of Mathematics or How to Provide Foundations for Abstract Mathematics.Jean-Pierre Marquis - 2012 - Review of Symbolic Logic 6 (1):51-75.
Relating First-Order Set Theories, Toposes and Categories of Classes.Steve Awodey, Carsten Butz, Alex Simpson & Thomas Streicher - 2014 - Annals of Pure and Applied Logic 165 (2):428-502.
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