Assaf Shani (Concordia University)

TITLE / TITRE

Classification using sets of sets of reals as invariants

ABSTRACT / RÉSUMÉ

The theory of Borel equivalence relations provides a rigorous framework to analyze the complexity of classification problems in mathematics, to determine when a successful classification is possible, and if so, to determine the optimal classifying invariants. Central to this theory are the iterated Friedman-Stanley jumps, which capture the complexity of classification using invariants which are countable sets of reals, countable sets of countable sets of reals, and so on. In this talk I will present structural dichotomies for the Friedman-Stanley jumps. This in turn provides a general tool for proving that a given classification problem is more difficult than the k'th Friedman-Stanley jump, for k=1,2,3,.... This extends results previously only known for the case k=1. The talk will begin by discussing the basic definitions and general goals behind the theory of Borel equivalence relations. We will discuss some known structure and non-structure results, and motivate these new dichotomies.

PLACE / LIEU
Hybride - CRM, Salle / Room 5340, Pavillon André Aisenstadt

ZOOM
https://us06web.zoom.us/j/84226701306?pwd=UEZ5NVpZaUlldW5qNU8vZzIvbEJXQT09