The strength of Borel Wadge comparability

Noam Greenberg (Victoria University of Wellington)

19-Apr-2021, 20:30-21:30 (3 years ago)

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.

logic

Audience: researchers in the topic


Computability theory and applications

Series comments: Description: Computability theory, logic

The goal of this endeavor is to run a seminar on the platform Zoom on a weekly basis, perhaps with alternating time slots each of which covers at least three out of four of Europe, North America, Asia, and New Zealand/Australia. While the meetings are always scheduled for Tuesdays, the timezone varies, so please refer to the calendar on the website for details about individual seminars.

Organizers: Damir Dzhafarov*, Vasco Brattka*, Ekaterina Fokina*, Ludovic Patey*, Takayuki Kihara, Noam Greenberg, Arno Pauly, Linda Brown Westrick
*contact for this listing

Export talk to