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. © 2009 Elsevier Inc. All rights reserved.

De Morgan classifying toposes

CARAMELLO, OLIVIA
2009-01-01

Abstract

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. © 2009 Elsevier Inc. All rights reserved.
2009
Boolean topos; Classifying topos; De Morgan topos; Geometric theory; Grothendieck topos; Mathematics (all)
Caramello, Olivia
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2063474
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