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Wednesday, October 09, 2024
12:00 PM - 1:00 PM
Online Event

Logic Seminar

Structurable equivalence relations and Lω1ωLω1ω interpretations
Ronnie Chen, Department of Mathematics, University of Michigan,

Please note that the time is PST

It is a folklore principle of locally countable Borel combinatorics that most arguments amount to doing countable combinatorics "in a uniform Borel way". We prove a result making this precise, by showing that there is a dual equivalence of categories between countable Borel equivalence relations (CBERs) and countable Lω1ωLω1ω theories admitting a (one-sorted) interpretation of the distinguished theory of Lusin–Novikov uniformizing functions together with a separating family of unary predicates. This allows all combinatorial concepts on CBERs to be characterized in terms of definability in countable structures, modulo said distinguished theory which describes structure available "for free" on every CBER. If time permits, I will also discuss a generalization of this correspondence to locally countable Borel groupoids. This is joint work with Rishi Banerjee.

For more information, please contact Math Dept. by phone at 626-395-4335 or by email at [email protected].