Vassilios Gregoriades - Classical versions of effective Borel uniformizations

This talk was part of the Workshop on "Reverse Mathematics and Higher Computability Theory" held at the ESI June 30 - July 4, 2025.

One of the most prominent applications of effective descriptive set theory is on the problem of uniformizing Borel sets by a Borel one. This is done by establishing (under some hypotheses) the existence of sufficiently definable points in the intersections of the given Borel set and by applying a general effective uniformization criterion. However strong the latter might be, it requires a solid recursion-theoretic background. We present a new approach to this topic, where recursion theory is reformulated in purely classical terms. This enables us to prove established facts in classical descriptive set theory using the effective ideas in a recursion-free language. Some examples include a classical version of the Effective Perfect Set Theorem and the Borel uniformization of a Borel set with countable sections. This talk is on joint ongoing work with Cordelia Tassopoulou.

Видео Vassilios Gregoriades - Classical versions of effective Borel uniformizations канала Erwin Schrödinger International Institute for Mathematics and Physics (ESI)