ADM Society Seminar, London, February 2025

Abstract: Mathematicians often try to classify objects of various kinds, for instance, groups up to isomorphism, graphs up to isomorphism, metric spaces up to isometry, and so on. What makes a classification problem tractable, and when is it hopeless? In this talk we will begin to show how set theory can help answer this question. The idea is to identify a classification problem with an equivalence relation, and then define a complexity hierarchy for equivalence relations.