Descriptive Set Theory and Modern Mathematical Analysis

A seminar talk given by Ned Wontner, University of Amsterdam, on March 15, 2024, 9 am, at Xiamen University Malaysia

Abstract:
This talk has two parts. In the first, more established part, I give an outline of some main motivations, ideas, and results in classical descriptive set theory. Throughout, I keep close to the historical roots in real analysis, notably the (classical) analysis of Baire functions. I mention Borel and analytic sets, and their regularity properties. In the second part, I gesture towards more recent work in generalized real analysis. I mention how descriptive set theory has been well generalized to higher cardinals, and look at one option to do the same for the real number ordered field. I state some generalizations, or lack thereof, of classical theorems of real analysis to these generalized real numbers, using various generalizations of continuity.