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An effective classification of Borel Wadge classes

  • Adam Day

    University of Auckland, Auckland, New Zealand

  • Noam Greenberg

    Victoria University of Wellington, Wellington, New Zealand
    ORCID

  • Matthew Harrison-Trainor

    University of Illinois Chicago, Chicago, USA

  • Dan Turetsky

    Victoria University of Wellington, Wellington, New Zealand
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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 of second-order arithmetic.

Cite this article

Adam Day, Noam Greenberg, Matthew Harrison-Trainor, Dan Turetsky, An effective classification of Borel Wadge classes. J. Eur. Math. Soc. (2025), published online first

DOI 10.4171/JEMS/1655