A q-wadge hierarchy in quasi-polish spaces

Journal of Symbolic Logic:1-26 (2020)
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Abstract

The wedge hierarchy was originally defined and studied only in the Baire space (and some other zero-dimensional spaces). Here we extend the Wadge hierarchy of Borel sets to arbitrary topological spaces by providing a set-theoretic definition of all its levels. We show that our extension behaves well in second countable spaces and especially in quasi-Polish spaces. In particular, all levels are preserved by continuous open surjections between second countable spaces which implies e.g. several Hausdorff-Kuratowski-type theorems in quasi-Polish spaces. In fact, many results hold not only for the Wadge hierarchy of sets but also for its extension to Borel functions from a space to a countable better quasiorder Q.

Other Versions

reprint Selivanov, Victor (2022) "A q-wadge hierarchy in quasi-polish spaces". Journal of Symbolic Logic 87(2):732-757

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References found in this work

Set Theory.K. Kuratowski & A. Mostowski - 1971 - Philosophy of Science 38 (2):314-315.
Quasi-Polish spaces.Matthew de Brecht - 2013 - Annals of Pure and Applied Logic 164 (3):356-381.
A Wadge hierarchy for second countable spaces.Yann Pequignot - 2015 - Archive for Mathematical Logic 54 (5):659-683.
Hierarchies of Δ 0 2 ‐measurable k‐partitions.Victor L. Selivanov - 2007 - Mathematical Logic Quarterly 53 (4-5):446-461.
Fine hierarchies via Priestley duality.Victor Selivanov - 2012 - Annals of Pure and Applied Logic 163 (8):1075-1107.

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