## An Outline of Algebraic Set Theory

### BibTeX

@MISC{Awodey_anoutline,

author = {Steve Awodey},

title = {An Outline of Algebraic Set Theory},

year = {}

}

### OpenURL

### Abstract

This survey 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, admitting adjustment in several respects to model different theories including classical, intuitionistic, bounded, and predicative ones. Under this scheme some familiar set theoretic properties are related to algebraic ones, like freeness, while others result from logical constraints, like definability. The overall theory is complete in two important respects: conventional elementary set theory axiomatizes algebraic framework itself are also complete with respect to a range of natural models consisting of “ideals ” of sets, suitably defined. Some previous results involving realizability, forcing, and sheaf models are