Complexity of the isomorphism relation for metric structures

Speaker(s)

Maciej Malicki

Affiliation

Warsaw School of Economics

Date

Feb. 27, 2019, 4:15 p.m.

Room

room 5050

Seminar

Topology and Set Theory Seminar

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For a given sentence s in the infinitary logic, one can consider the Borel space M of all countable models satisfying s, and the isomorphism equivalence relation E on M. Hjorth and Kechris found a natural characterization in model-theoretic terms of the situations when E is smooth or essentially countable. We generalize their results to the context of Polish metric structures, and we give a short proof of a theorem of Kechris to the effect that orbit equivalence relations induced by continuous actions of locally compact groups are essentially countable. This is joint work in progress with Todor Tsankov.

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