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Martina Pfeifer

Luca Motto Ros (Turin): A descriptive main gap theorem

Friday, 07.06.2019 11:00 im Raum SR 1D

Mathematik und Informatik

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>20. 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.



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