Speaker Introduction

Dr. Ned Wontner was a Postdoctoral Scholar at Universiteit van Amsterdam, ILLC. He was graduated from Universiteit van Amsterdam, ILLC 2023. Dr. Ned Wontner got his Master on Non-Standard Analysis at University of Cambridge 2019, and his Bachelor at University of Oxford 2017.

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.