589 research outputs found
De Morgan classifying toposes
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.Comment: 37 page
Topologies for intermediate logics
We investigate the problem of characterizing the classes of Grothendieck
toposes whose internal logic satisfies a given assertion in the theory of
Heyting algebras, and introduce natural analogues of the double negation and De
Morgan topologies on an elementary topos for a wide class of intermediate
logics.Comment: 21 page
De Morgan's law and the theory of fields
We show that the classifying topos for the theory of fields does not satisfy
De Morgan's law, and we identify its largest dense De Morgan subtopos as the
classifying topos for the theory of fields of nonzero characteristic which are
algebraic over their prime fields
Cyclic theories
We describe a geometric theory classified by Connes-Consani's epicylic topos
and two related theories respectively classified by the cyclic topos and by the
topos .Comment: 25 page
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