The isomorphism relation of unsuperstable theories in the generalized Borel-reducibility hierarchy

26.04.2022 15:00 - 16:30

M. Moreno (U Wien)

One of the most important questions in generalized descriptive set theory is whether there is a generalized Borel-reducibility counterpart of Shelah's main gap theorem? (i.e. for any classifiable theory \(T\) and nonclassifiable theory \(T'\), is the isomorphism relation of \(T\) Borel reducible to the isomorphism relation of \(T'\)?) In this talk we will study the case of unsuperstable theories. By introducing the notion of \(K\)-colorable linear orders we can construct generalized Ehrenfeucht-Mostowski models and a Borel reduction from the isomorphism relation of any classifiable theory to the isomorphism relation of any unsuperstable theory.




SR 10, 1. Stock, Koling. 14-16, 1090 Wien