| Time: | 12:00 - 13:20 |
| Room: |
Wean Hall 7201
|
| Speaker: |
Alexei Kolesnikov Department of Mathematics Towson University |
| Title: |
Generalized Martin's axiom and disjoint amalgamation
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| Abstract: | In a joint work with Baldwin and Shelah, we construct examples of abstract elementary classes that have the disjoint amalgamation property for models of size up to $\beth_\alpha$, but ultimately failing to have the disjoint amalgamation for sufficiently large models. The argument relies on a set-theoretic principle introduced by Shelah. A form of that principle was used by Shelah to study simple unstable theories. |