Luca Motto Ros (Turin): A descriptive main gap theorem
Friday, 07.06.2019 11:00 im Raum SR 1D
Answering a question of S. Friedman, Hyttinen and Kulikov, we
show that there is a tight connection between the depth of a classifiable shallow theory $T$ and the Borel rank of the isomorphism relation $\cong^\kappa_T$ on its models of size $\kappa$, for $\kappa$ any cardinal satisfying $\kappa^{< \kappa} = \kappa > 2^{\aleph_0}$. This yields a descriptive set-theoretical analogue of Shelah?s Main Gap Theorem. We also discuss some limitations to the possible (Borel) complexities of $\cong^\kappa_T$, and provide a characterization of categoricity of $T$ in
terms of the descriptive set-theoretical complexity of $\cong^\kappa_T$.
Joint work with F. Mangraviti.
Angelegt am Wednesday, 29.05.2019 09:12 von Martina Pfeifer
Geändert am Wednesday, 29.05.2019 09:12 von Martina Pfeifer
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