An Effective Classification of Borel Wadge Classes

TL;DR

This paper introduces a new effective classification of Borel Wadge classes in Baire space, utilizing true stage machinery to provide new proofs of separation and determinacy results within second-order arithmetic.

Contribution

It offers a novel classification method for Borel Wadge classes and new proofs of key theorems using true stage machinery.

Findings

Effective classification of Borel Wadge classes

New proof of Louveau and Saint-Raymond's separation theorem

Borel Wadge determinacy established in ATR_0 + Pi^1_1-I subsystem

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 Montalb\'an. 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 $\text{ATR}_0+\Pi^1_1$-I of second-order arithmetic.