We will continue on Thursday, October 3, in M5 at 1pm by the talk
P. Arndt
Ranges of functors and geometric elementary classes
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 image of F satisfy first order sentences other than those of T, or whether the essential image of F can be described as Mod(T') for an extension T' of T. If Mod(S), Mod(T) are kaccessible and F is a strongly kaccessible functor for some cardinal k, we can give criteria for this in the realm of Espíndola's kgeometric first order theories. To this end we consider kclassifying toposes associated to S and T. The hypotheses ensure that the functor F is induced by a kgeometric essential morphism between them. The criteria are then obtained by factorizing this geometric morphism appropriately. We will explain the involved notions and give examples and applications.
