منابع مشابه
Predicative Algebraic Set Theory
In this paper the machinery and results developed in [Awodey et al, 2004] are extended to the study of constructive set theories. Specifically, we introduce two constructive set theories BCST and CST and prove that they are sound and complete with respect to models in categories with certain structure. Specifically, basic categories of classes and categories of classes are axiomatized and shown...
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We suggest a new basic framework for the Weyl-Feferman predicativist program by constructing a formal predicative set theory PZF which resembles ZF . The basic idea is that the predicatively acceptable instances of the comprehension schema are those which determine the collections they define in an absolute way, independent of the extension of the “surrounding universe”. This idea is implemente...
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We show how one may establish proof-theoretic results for constructive Zermelo-Fraenkel set theory, such as the compactness rule for Cantor space and the Bar Induction rule for Baire space, by constructing sheaf models and using their preservation properties.
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This is the third installment in a series of papers on algebraic set theory. In it, we develop a uniform approach to sheaf models of constructive set theories based on ideas from categorical logic. The key notion is that of a “predicative category with small maps” which axiomatises the idea of a category of classes and class morphisms, together with a selected class of maps whose fibres are set...
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This paper is the second in a series on the relation between algebraic set theory [19] and predicative formal systems. The purpose of the present paper is to show how realizability models of constructive set theories fit into the framework of algebraic set theory. It can be read independently from the first part [5]; however, we recommend that readers of this paper read the introduction to [5],...
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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 1994
ISSN: 0029-4527
DOI: 10.1305/ndjfl/1094061860