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Algebraic models of intuitionistic theories of sets and classes

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S. Awodey and H. Forssell

This paper constructs models of intuitionistic set theory in suitable
categories. First, a Basic Intuitionistic Set Theory (BIST) is
stated, and the categorical semantics are given. Second, we give a
notion of an *ideal* over a category, using which one can build
a model of BIST in which a given topos occurs as the sets. And
third, a sheaf model is given of a Basic Intuitionistic Class Theory
conservatively extending BIST. The paper extends the results in
Awodey, Butz, Simpson and Streicher (2003) by
introducing a new and perhaps more natural notion of ideal, and in
the class theory of part three.

Keywords:
algebraic set theory, topos theory, sheaf theory

2000 MSC:
18B05, 18B25, 18C10, 03G30, 03E70, 03F60

*Theory and Applications of Categories,*
Vol. 15, CT2004,
No. 5, pp 147-163.

http://www.tac.mta.ca/tac/volumes/15/5/15-05.dvi

http://www.tac.mta.ca/tac/volumes/15/5/15-05.ps

http://www.tac.mta.ca/tac/volumes/15/5/15-05.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/15/5/15-05.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/15/5/15-05.ps

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