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Logic Seminar

Monday, March 8, 2021
12:00pm to 1:00pm
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Online Event
Infinitary continuous logic and descriptive set theory
Maciej Malicki, Department of Foundations of Mathematics, IMPAN,

There are deep connections between model theory of the infinitary logic Lω1ω and descriptive set theory: Scott analysis, the López-Escobar theorem or the Suzuki theorem are well known examples of this phenomenon. In this talk, I would like to present results of an ongoing research devoted to generalizing these connections to the setting of continuous infinitary logic and Polish metric structures. In particular, I will discuss a continuous counterpart of a theorem of Hjorth and Kechris characterizing essential countability of the isomorphism relation on a given Borel class of countable structures. As an application, I will give a short model-theoretic proof of a result of Kechris saying that orbit equivalence relations induced by continuous actions of locally compact Polish groups are essentially countable. This is joint work with Andreas Hallbäck and Todor Tsankov.

For more information, please email A. Kechris at [email protected].