|Time:|| 12:00 - 13:20
Doherty Hall 4303
Kurt Gödel Research Center for Mathematical Logic
University of Vienna
Classification Theory of Homogeneous Model Theory vs Constructibility of Potentially Isomorphic Pairs
The work presented is joint with S-D Friedman and T Hyttinen. Our aim was to generalize a very nice result of Friedman, Hyttinen, and Rautila which tied first-order model theoretic classification theory to constructibility under the assumption of 0#, to a non-elementary model theoretic setting. The original result stated:
Theorem. Assume 0# exists and let T be a constructible first-orer 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 real-preserving 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/non-structure 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.