9 found
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  1.  22
    Questions on generalised Baire spaces.Yurii Khomskii, Giorgio Laguzzi, Benedikt Löwe & Ilya Sharankou - 2016 - Mathematical Logic Quarterly 62 (4-5):439-456.
    We provide a list of open problems in the research area of generalised Baire spaces, compiled with the help of the participants of two workshops held in Amsterdam (2014) and Hamburg (2015).
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  2.  40
    Regularity properties on the generalized reals.Sy David Friedman, Yurii Khomskii & Vadim Kulikov - 2016 - Annals of Pure and Applied Logic 167 (4):408-430.
  3.  22
    Full-splitting Miller trees and infinitely often equal reals.Yurii Khomskii & Giorgio Laguzzi - 2017 - Annals of Pure and Applied Logic 168 (8):1491-1506.
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  4.  34
    Cichoń’s diagram, regularity properties and $${\varvec{\Delta}^1_3}$$ Δ 3 1 sets of reals.Vera Fischer, Sy David Friedman & Yurii Khomskii - 2014 - Archive for Mathematical Logic 53 (5-6):695-729.
    We study regularity properties related to Cohen, random, Laver, Miller and Sacks forcing, for sets of real numbers on the Δ31\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\Delta}^1_3}$$\end{document} level of the projective hieararchy. For Δ21\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\Delta}^1_2}$$\end{document} and Σ21\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\Sigma}^1_2}$$\end{document} sets, the relationships between these properties follows the pattern of the well-known Cichoń diagram for cardinal characteristics of the continuum. It is known that (...)
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  5.  25
    Mad Families Constructed from Perfect Almost Disjoint Families.Jörg Brendle & Yurii Khomskii - 2013 - Journal of Symbolic Logic 78 (4):1164-1180.
  6.  19
    Paraconsistent and Paracomplete Zermelo–Fraenkel Set Theory.Yurii Khomskii & Hrafn Valtýr Oddsson - forthcoming - Review of Symbolic Logic:1-31.
    We present a novel treatment of set theory in a four-valued paraconsistent and paracomplete logic, i.e., a logic in which propositions can be both true and false, and neither true nor false. Our approach is a significant departure from previous research in paraconsistent set theory, which has almost exclusively been motivated by a desire to avoid Russell’s paradox and fulfil naive comprehension. Instead, we prioritise setting up a system with a clear ontology of non-classical sets, which can be used to (...)
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  7.  72
    Co-analytic mad families and definable wellorders.Vera Fischer, Sy David Friedman & Yurii Khomskii - 2013 - Archive for Mathematical Logic 52 (7-8):809-822.
    We show that the existence of a ${\Pi^1_1}$ -definable mad family is consistent with the existence of a ${\Delta^{1}_{3}}$ -definable well-order of the reals and ${\mathfrak{b}=\mathfrak{c}=\aleph_3}$.
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  8.  25
    Polarized partitions on the second level of the projective hierarchy.Jörg Brendle & Yurii Khomskii - 2012 - Annals of Pure and Applied Logic 163 (9):1345-1357.
  9.  50
    Projective Hausdorff gaps.Yurii Khomskii - 2014 - Archive for Mathematical Logic 53 (1-2):57-64.
    Todorčević (Fund Math 150(1):55–66, 1996) shows that there is no Hausdorff gap (A, B) if A is analytic. In this note we extend the result by showing that the assertion “there is no Hausdorff gap (A, B) if A is coanalytic” is equivalent to “there is no Hausdorff gap (A, B) if A is ${{\bf \it{\Sigma}}^{1}_{2}}$ ”, and equivalent to ${\forall r \; (\aleph_1^{L[r]}\,< \aleph_1)}$ . We also consider real-valued games corresponding to Hausdorff gaps, and show that ${\mathsf{AD}_\mathbb{R}}$ for pointclasses (...)
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