De Morgan classifying toposes

Details De Morgan classifying toposes De Morgan classifying toposes

2008-08-11

arxiv.org/abs/0808.1519v1

Mathematics

Category Theory

37 pages

Scientific paper

We present a general method for deciding whether a Grothendieck topos satisfies De Morgan's law (resp. the law of excluded middle) or not; applications to the theory of classifying toposes follow. Specifically, we obtain a syntactic characterization of the class of geometric theories whose classifying toposes satisfy De Morgan's law (resp. are Boolean), as well as model-theoretic criteria for theories whose classifying toposes arise as localizations of a given presheaf topos.

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