Classification problems from the descriptive set theoretical perspective

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.

arXiv commentSurvey paper on Borel reducibility and classification problems. 26 pages. Accepted for publication in the collection Research Trends in Contemporary Logic (edited by Melvin Fitting, Dov Gabbay, Massoud Pourmahdian, Adrian Rezus, and Ali Sadegh Daghighi)

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• Measure reducibility of countable Borel equivalence relations
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• The complexity of the embeddability relation between torsion-free abelian groups of uncountable size