Takako Nemoto (Japan Advanced Institute of Science and Technology)
Peter Arndt (Heinrich-Heine-Universität Düsseldorf)
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 first-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. The involved notions will be explained and examples will be given.