The Feldman-Moore, Glimm-Effros, and Lusin-Novikov theorems over quotients

TL;DR

This paper extends fundamental theorems in descriptive set theory from Polish spaces to their quotients under Borel orbit equivalence relations, broadening their applicability.

Contribution

It generalizes key theorems—Feldman-Moore, Glimm-Effros, and Lusin-Novikov—to quotient spaces formed by Borel orbit equivalence relations.

Findings

Generalized the Feldman-Moore theorem to quotient spaces.

Extended the Glimm-Effros dichotomy to quotients.

Adapted the Lusin-Novikov uniformization theorem for quotients.

Abstract

We establish generalizations of the Feldman-Moore theorem, the Glimm-Effros dichotomy, and the Lusin-Novikov uniformization theorem from Polish spaces to their quotients by Borel orbit equivalence relations.