David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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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
David Corfield (2011). Understanding the Infinite II: Coalgebra. Studies in History and Philosophy of Science Part A 42 (4):571-579.
Gregory Wheeler (2013). Models, Models, and Models. Metaphilosophy 44 (3):293-300.
Jean-Pierre Marquis (2013). Categorical Foundations of Mathematics or How to Provide Foundations for Abstract Mathematics. Review of Symbolic Logic 6 (1):51-75.
Steve Awodey, Carsten Butz, Alex Simpson & Thomas Streicher (2014). Relating First-Order Set Theories, Toposes and Categories of Classes. Annals of Pure and Applied Logic 165 (2):428-502.
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