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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, such as 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.<\/jats:p>","DOI":"10.2178\/bsl\/1231081369","type":"journal-article","created":{"date-parts":[[2009,1,4]],"date-time":"2009-01-04T15:03:06Z","timestamp":1231081386000},"page":"281-298","source":"Crossref","is-referenced-by-count":10,"title":["A Brief Introduction to Algebraic Set Theory"],"prefix":"10.1017","volume":"14","author":[{"given":"Steve","family":"Awodey","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,1,15]]},"reference":[{"key":"S107989860000158X_ref003","unstructured":"Algebraic set theory, www.phil.cmu.edu\/projects\/ast."},{"key":"S107989860000158X_ref016","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(83)90085-3"},{"key":"S107989860000158X_ref043","first-page":"77","article-title":"Elementary axioms for categories of classes","volume":"1999","author":"Simpson","journal-title":"Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science"},{"key":"S107989860000158X_ref037","unstructured":"Mccarty D. 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