Logic Seminar

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.