An Effective Classification of Borel Wadge Classes

2022/11/15 by Adam R. Day, Noam Greenberg, Day, Adam +5
Computer Science · Mathematics · #03D99 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2211.07961

openalex publication_date 2022/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a new and effective classification of all Borel Wadge classes of subsets of Baire space. This relies on the true stage machinery originally developed by Montalbán. We use this machinery to give a new proof of Louveau and Saint-Raymond's separation theorem for Borel Wadge classes. This gives a proof of Borel Wadge determinacy in the subsystem ATR₀+Π¹₁-I of second-order arithmetic.

Related

• Constructing Wadge classes
• Bad Wadge-like reducibilities on the Baire space
• The Wadge order on the Scott domain is not a well-quasi-order
• Potential Wadge classes
• A syntactic approach to Borel functions: Some extensions of Louveau's theorem