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  1.  40
    Hierarchies of [ ... ] º 2-Measurable K -Partitions.Victor L. Selivanov - 2007 - Mathematical Logic Quarterly 53 (4-5):446-461.
    Attempts to extend the classical Hausdorff difference hierarchy to the case of partitions of a space to k > 2 subsets lead to non-equivalent notions. In a hope to identify the right extension we consider the extensions appeared in the literature so far: the limit-, level-, Boolean and Wadge hierarchies of k -partitions. The advantages and disadvantages of the four hierarchies are discussed. The main technical contribution of this paper is a complete characterization of the Wadge degrees of [ ¿ (...)
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  2.  7
    Turing Reducibility in the Fine Hierarchy.Alexander G. Melnikov, Victor L. Selivanov & Mars M. Yamaleev - 2020 - Annals of Pure and Applied Logic 171 (7):102766.
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  3. Recursiveness of Ω‐Operations.Victor L. Selivanov - 1994 - Mathematical Logic Quarterly 40 (2):204-206.
    It is well known that any finitary operation is recursive in a suitable total numeration. A. Orlicki showed that there is an ω-operation not recursive in any total numeration. We will show that any ω-operation is recursive in a partial numeration.
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  4.  17
    Hierarchies in Φ‐Spaces and Applications.Victor L. Selivanov - 2005 - Mathematical Logic Quarterly 51 (1):45-61.
    We establish some results on the Borel and difference hierarchies in φ-spaces. Such spaces are the topological counterpart of the algebraic directed-complete partial orderings. E.g., we prove analogs of the Hausdorff Theorem relating the difference and Borel hierarchies and of the Lavrentyev Theorem on the non-collapse of the difference hierarchy. Some of our results generalize results of A. Tang for the space Pω. We also sketch some older applications of these hierarchies and present a new application to the question of (...)
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  5.  4
    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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