The associated sheaf functor theorem in algebraic set theory

Annals of Pure and Applied Logic 156 (1):68-77 (2008)

We prove a version of the associated sheaf functor theorem in Algebraic Set Theory. The proof is established working within a Heyting pretopos equipped with a system of small maps satisfying the axioms originally introduced by Joyal and Moerdijk. This result improves on the existing developments by avoiding the assumption of additional axioms for small maps and the use of collection sites
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DOI 10.1016/j.apal.2008.06.008
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References found in this work BETA

Aspects of General Topology in Constructive Set Theory.Peter Aczel - 2006 - Annals of Pure and Applied Logic 137 (1):3-29.
Independence Results Around Constructive ZF.Robert S. Lubarsky - 2005 - Annals of Pure and Applied Logic 132 (2-3):209-225.
Heyting-Valued Interpretations for Constructive Set Theory.Nicola Gambino - 2006 - Annals of Pure and Applied Logic 137 (1):164-188.

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Citations of this work BETA

Lawvere-Tierney Sheaves in Algebraic Set Theory.S. Awodey, N. Gambino & M. A. Warren - 2009 - Journal of Symbolic Logic 74 (3):861 - 890.

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