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Logic Seminar

Wednesday, May 25, 2022
12:00pm to 1:00pm
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Online Event
Classifying invariants for E1E1
Assaf Shani, Department of Mathematics, Harvard University,

We introduce a framework for studying "reasonable" classifying invariants, more permitting than "classification by countable structures". This framework respects the intuitions and results about classifications by countable structures, and allows for equivalence relations such as E1E1 and E+1E1+ to be "reasonably classifiable" as well. In this framework we show that E1E1 has classifying invariants which are κκ-sequences of E0E0-classes for κ=bκ=b, and it does not have such classifying invariants if κ<add(B)κ<add(B).
The result relies on analysing the tail intersection model ⋂n<ωV[cn,cn+1,…]⋂n<ωV[cn,cn+1,…], where ⟨c0,c1,…⟩⟨c0,c1,…⟩ is a generic sequence of Cohen reals.

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