9 found
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  1.  13
    Regularity Properties on the Generalized Reals.Sy David Friedman, Yurii Khomskii & Vadim Kulikov - 2016 - Annals of Pure and Applied Logic 167 (4):408-430.
  2.  14
    On Σ11-Complete Equivalence Relations on the Generalized Baire Space.Tapani Hyttinen & Vadim Kulikov - 2015 - Mathematical Logic Quarterly 61 (1-2):66-81.
  3.  4
    Preferential Engagement and What Can We Learn from Online Chess?Vadim Kulikov - 2020 - Minds and Machines 30 (4):617-636.
    An online game of chess against a human opponent appears to be indistinguishable from a game against a machine: both happen on the screen. Yet, people prefer to play chess against other people despite the fact that machines surpass people in skill. When the philosophers of 1970’s and 1980’s argued that computers will never surpass us in chess, perhaps their intuitions were rather saying “Computers will never be favored as opponents”? In this paper we analyse through the introduced concepts of (...)
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  4.  10
    A Generalized Borel-Reducibility Counterpart of Shelah’s Main Gap Theorem.Tapani Hyttinen, Vadim Kulikov & Miguel Moreno - 2017 - Archive for Mathematical Logic 56 (3-4):175-185.
    We study the κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa $$\end{document}-Borel-reducibility of isomorphism relations of complete first order theories in a countable language and show the consistency of the following: For all such theories T and T′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T^{\prime }$$\end{document}, if T is classifiable and T′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T^{\prime }$$\end{document} is not, then the isomorphism of models of T′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} (...)
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  5.  12
    Failures of the Silver Dichotomy in the Generalized Baire Space.Sy-David Friedman & Vadim Kulikov - 2015 - Journal of Symbolic Logic 80 (2):661-670.
    We prove results that falsify Silver’s dichotomy for Borel equivalence relations on the generalized Baire space under the assumptionV=L.
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  6.  5
    Borel Reductions and Cub Games in Generalised Descriptive Set Theory.Vadim Kulikov - 2013 - Journal of Symbolic Logic 78 (2):439-458.
    It is shown that the power set of $\kappa$ ordered by the subset relation modulo various versions of the non-stationary ideal can be embedded into the partial order of Borel equivalence relations on $2^\kappa$ under Borel reducibility. Here $\kappa$ is an uncountable regular cardinal with $\kappa^{<\kappa}=\kappa$.
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  7. Borel $$^{*}$$ Sets in the Generalized Baire Space and Infinitary Languages.Vadim Kulikov & Tapani Hyttinen - 2018 - In Hans van Ditmarsch & Gabriel Sandu (eds.), Jaakko Hintikka on Knowledge and Game Theoretical Semantics. Springer.
    We start by giving a survey to the theory of $${\text {Borel}}^{*}$$ sets in the generalized Baire space $${\text {Baire}}=\kappa ^{\kappa }$$. In particular we look at the relation of this complexity class to other complexity classes which we denote by $${\text {Borel}}$$, $${\Delta _1^1}$$ and $${\Sigma _1^1}$$ and the connections between $${\text {Borel}}^*$$ sets and the infinitely deep language $$M_{\kappa ^+\kappa }$$. In the end of the paper we will prove the consistency of $${\text {Borel}}^{*}\ne \Sigma ^{1}_{1}$$.
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  8.  7
    Reducibility of Equivalence Relations Arising From Nonstationary Ideals Under Large Cardinal Assumptions.David Asperó, Tapani Hyttinen, Vadim Kulikov & Miguel Moreno - 2019 - Notre Dame Journal of Formal Logic 60 (4):665-682.
    Working under large cardinal assumptions such as supercompactness, we study the Borel reducibility between equivalence relations modulo restrictions of the nonstationary ideal on some fixed cardinal κ. We show the consistency of Eλ-clubλ++,λ++, the relation of equivalence modulo the nonstationary ideal restricted to Sλλ++ in the space λ++, being continuously reducible to Eλ+-club2,λ++, the relation of equivalence modulo the nonstationary ideal restricted to Sλ+λ++ in the space 2λ++. Then we show that for κ ineffable Ereg2,κ, the relation of equivalence modulo (...)
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  9.  1
    Borel\documentclass[12pt]{Minimal} \usepackage{Amsmath} \usepackage{Wasysym} \usepackage{Amsfonts} \usepackage{Amssymb} \usepackage{Amsbsy} \usepackage{Mathrsfs} \usepackage{Upgreek} \setlength{\oddsidemargin}{-69pt} \begin{Document}$$^{*}$$\end{Document} Sets in the Generalized Baire Space and Infinitary Languages. [REVIEW]Tapani Hyttinen & Vadim Kulikov - 2018 - In Hans van Ditmarsch & Gabriel Sandu (eds.), Jaakko Hintikka on Knowledge and Game Theoretical Semantics. Springer. pp. 395-412.
    We start by giving a survey to the theory of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {Borel}}^{*}$$\end{document} sets in the generalized Baire space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {Baire}}=\kappa ^{\kappa }$$\end{document}. In particular we look at the relation of this complexity class to other complexity classes which we denote by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {Borel}}$$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta _1^1}$$\end{document} (...)
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