A brief introduction to algebraic set theory

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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DOI 10.2178/bsl/1231081369
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Wellfounded Trees in Categories.Ieke Moerdijk & Erik Palmgren - 2000 - Annals of Pure and Applied Logic 104 (1-3):189-218.

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Understanding the Infinite II: Coalgebra.David Corfield - 2011 - Studies in History and Philosophy of Science Part A 42 (4):571-579.
Models, Models, and Models.Gregory Wheeler - 2013 - Metaphilosophy 44 (3):293-300.

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