Bernays-Gödel type theory (2003) [6 citations — 0 self]
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by Carsten Butz
Journal of Pure and Applied Algebra
http://euclid.math.mcgill.ca/butz/preprints/axiomatics-a4.ps.gz
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Abstract:
Abstract. There is a close relationship between category theory and logic. For example, elementary toposes have just enough properties to interpret intuitionistic higher-order logic, and we think of toposes as `categories of sets'. In fact, a topos with a natural numbers object is an adequate universe in which to develop intuitionistic mathematics, and such a topos may be seen as a categorical analogue of a model of intuitionistic Zermelo-Fraenkel set-theory. In this paper we implement the categorical analogue of Bernays-Godel set-theory. We introduce the notion of small structure on a category, and if small structure satises certain axioms we can think of the underlying category as a category of classes. Our axioms imply the
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