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Seminario: “Ranges of functors and elementary classes via topos theory”

Giovedì 14 Febbraio 2019, ore 17:00 - Aula 2AB40 - Peter Arndt

ARGOMENTI: Seminars

Giovedì 14 Febbraio 2019 alle ore 17:00 in Aula 2AB40, Peter Arndt (University of Düsseldorf) terrà un seminario dal titolo “Ranges of functors and elementary classes via topos theory”.

Abstract
Given first order theories S,T and a functor F:Mod(S)-->Mod(T) between their categories of models, one can ask whether objects in the range of F satisfy 1st order sentences other than those of T, and whether the essential image of F is an elementary class. Under certain conditions on F we can give criteria for this for so-called k-geometric first order sentences and k-geometric elementary classes. These criteria are obtained by considering classifying toposes associated to S and T, such that F is induced by a geometric morphism between them, and then factorizing this geometric morphism appropriately. We will explain the involved notions and give examples.