Compact Structures in Descriptive Classification Theory
Joseph Zielinski · Bulletin of Symbolic Logic · 2018
a positive answer to this question for an arbitrary group Γ.I also prove that a 4-set generator always exists off of a (topologically) meager set, thus answering a question of A. Kechris from the mid-90s.Lastly, I show that any aperiodic action of Γ admits a Γ-equivariant Borel map to the aperiodic part of the 2-shift.Part 2: We investigate pairs of countable Borel equivalence relations E ⊆ F , where E is of finite index in F .Our main focus is the well-known problem of whether the treeability of E implies that of F : we provide various reformulations of it and reduce it to one natural universal example.In the measure-theoretic context, assuming that F is ergodic, we characterize the case when E is normal.Finally, in the ergodic case, we characterize the equivalence relations that arise from almost free actions of virtually free groups.Part 3: We consider natural complexity measures for recursive programs from given primitives and derive inequalities between them, answering a question asked by Yiannis Moschovakis.