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 ≅κT on its models of size κ, for κ any cardinal satisfying κ<κ=κ>2ℵ0. This yields a descriptive set-theoretical analogue of Shelah?s Main Gap Theorem. We also discuss some limitations to the possible (Borel) complexities of ≅κT, and provide a characterization of categoricity of T in
terms of the descriptive set-theoretical complexity of ≅κT.
Joint work with F. Mangraviti.
Angelegt am 29.05.2019 von Martina Pfeifer
Geändert am 29.05.2019 von Martina Pfeifer
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