February 4, 2019

Monday, 11 February 2019, Sala Verde.

Both talks have been recorded.


Takako Nemoto (Japan Advanced Institute of Science and Technology)

Systems for constructive reverse mathematics abstract


Peter Arndt (Heinrich-Heine-Universität Düsseldorf)

Ranges of functors and elementary classes via topos theory

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.