Time:  12:00  13:20 
Room: 
Doherty Hall 4303

Speaker: 
Agatha WalczakTypke Kurt Gödel Research Center for Mathematical Logic University of Vienna 
Title: 
Classification Theory of Homogeneous Model Theory vs Constructibility of Potentially Isomorphic Pairs

Abstract: 
The work presented is joint with SD Friedman and T Hyttinen. Our aim was to generalize a very nice result of Friedman, Hyttinen, and Rautila which tied firstorder model theoretic classification theory to constructibility under the assumption of 0#, to a nonelementary model theoretic setting. The original result stated: Theorem. Assume 0# exists and let T be a constructible firstorer theory which is countable in the constructible universe L. Let kappa be a cardinal in L larger than (aleph_1)^L. Then the collection of constructible pairs of models A,B of T, A,B=kappa, which are isomorphic in a cardinal and realpreserving extension of L is itself constructible if and only if T is classifiable (i.e. superstable with NDOP and NOTOP). We have chosen Homogeneous Model Theory as a good setting for generalizing this result because of the already well developed structure/nonstructure theory in this setting. I will present the result for Homogeneous Model Theory analogous to the theorem above, and discuss some of the issues involved in the proof. 