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  1. A q-wadge hierarchy in quasi-polish spaces.Victor Selivanov - 2020 - Journal of Symbolic Logic:1-26.
    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, (...)
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  • A q-wadge hierarchy in quasi-polish spaces.Victor Selivanov - 2022 - Journal of Symbolic Logic 87 (2):732-757.
    The Wadge hierarchy was originally defined and studied only in the Baire space. 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 (...)
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  • Fraïssé’s conjecture in [math]-comprehension.Antonio Montalbán - 2017 - Journal of Mathematical Logic 17 (2):1750006.
    We prove Fraïssé’s conjecture within the system of Π11-comprehension. Furthermore, we prove that Fraïssé’s conjecture follows from the Δ20-bqo-ness of 3 over the system of Arithmetic Transfinite Recursion, and that the Δ20-bqo-ness of 3 is a Π21-statement strictly weaker than Π11-comprehension.
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  • Definability in the h -quasiorder of labeled forests.Oleg V. Kudinov, Victor L. Selivanov & Anton V. Zhukov - 2009 - Annals of Pure and Applied Logic 159 (3):318-332.
    We prove that for any k≥3 each element of the h-quasiorder of finite k-labeled forests is definable in the ordinary first order language and, respectively, each element of the h-quasiorder of countable k-labeled forests is definable in the language Lω1ω, in both cases provided that the minimal non-smallest elements are allowed as parameters. As corollaries, we characterize the automorphism groups of both structures and show that the structure of finite k-forests is atomic. Similar results hold true for two other relevant (...)
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  • A syntactic approach to Borel functions: some extensions of Louveau’s theorem.Takayuki Kihara & Kenta Sasaki - 2023 - Archive for Mathematical Logic 62 (7):1041-1082.
    Louveau showed that if a Borel set in a Polish space happens to be in a Borel Wadge class $$\Gamma $$, then its $$\Gamma $$ -code can be obtained from its Borel code in a hyperarithmetical manner. We extend Louveau’s theorem to Borel functions: If a Borel function on a Polish space happens to be a $$ \underset{\widetilde{}}{\varvec{\Sigma }}\hbox {}_t$$ -function, then one can find its $$ \underset{\widetilde{}}{\varvec{\Sigma }}\hbox {}_t$$ -code hyperarithmetically relative to its Borel code. More generally, we prove (...)
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  • Closed choice and a uniform low basis theorem.Vasco Brattka, Matthew de Brecht & Arno Pauly - 2012 - Annals of Pure and Applied Logic 163 (8):986-1008.
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