Classification problems from the descriptive set theoretical perspective

TL;DR

This paper reviews recent advances in classification problems using Borel reducibility from a descriptive set theoretical perspective, highlighting developments over the past decade since Kechris's influential survey.

Contribution

It provides an updated overview of (anti-)classification results in descriptive set theory, focusing on Borel reducibility and its extensions to uncountable cardinals.

Findings

Summary of key (anti-)classification results in the last decade

Analysis of Borel reducibility applications to uncountable cardinals

Identification of open problems and future directions

Abstract

Twenty years have passed since Kechris' seminal survey paper [A. S. Kechris, New directions in descriptive set theory. Bull. Symbolic Logic, 5(2):161-174, 1999]. As a follow-up of that work, we review some ot the (anti-)classification results that have been obtained in the last decade using Borel reducibility and its generalizations to uncountable cardinals.