Midwest Computability Seminar

XXVI
Part vi


The Midwest Computability Seminar is meeting remotely in the winter and spring of 2021. The recurring Zoom link is:

https://notredame.zoom.us/j/99754332165?pwd=RytjK1RFZU5KWnZxZ3VFK0g4YTMyQT09

Meeting ID: 997 5433 2165

Passcode: midwest


slides    Panopto video    YouTube video


This session will be held jointly with the Computability Theory and Applications Online Seminar.


DATE: Monday, April 19th, 2021

TIME: 3:30 - 4:30 PM Central Time

SPEAKER: Noam Greenberg - Victoria University of Wellington

TITLE: The strength of Borel Wadge comparability

ABSTRACT: Wadge's comparability lemma says that the Borel sets are almost linearly ordered under Wadge reducibility: for any two Borel sets A and B, either A is a continuous pre-image of B, or B is a continuous pre-image of the complement of A. Wadge's proof uses Borel determinacy, which is not provable in second order arithmetic (H. Friedman). Using deep and complex techniques, Louveau and Saint-Raymond showed that Borel Wadge comparability is provable in second order arithmetic, but did not explore its precise proof-theoretic strength. I will discuss recent work aiming to clarify this.

One of the main technical tools we use is Montalbán’s “true stage” machinery, originally developed for iterated priority constructions in computable structure theory, but more recently used by Day and Marks for their resolution of the decomposability conjecture.

Joint work with Adam Day, Matthew Harrison-Trainor, and Dan Turetsky.



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