An Effective Classification of Borel Wadge Classes

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