14 found
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  1.  23
    Two chain conditions and their Todorčević's fragments of Martin's Axiom.Teruyuki Yorioka - 2024 - Annals of Pure and Applied Logic 175 (1):103320.
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  2.  52
    The cofinality of the strong measure zero ideal.Teruyuki Yorioka - 2002 - Journal of Symbolic Logic 67 (4):1373-1384.
    We give a characterization of the cofinality of the strong measure zero ideal under the continuum hypothesis and prove that we can force it to a value less than the power of the continuum.
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  3.  78
    A non-implication between fragments of Martin’s Axiom related to a property which comes from Aronszajn trees.Teruyuki Yorioka - 2010 - Annals of Pure and Applied Logic 161 (4):469-487.
    We introduce a property of forcing notions, called the anti-, which comes from Aronszajn trees. This property canonically defines a new chain condition stronger than the countable chain condition, which is called the property . In this paper, we investigate the property . For example, we show that a forcing notion with the property does not add random reals. We prove that it is consistent that every forcing notion with the property has precaliber 1 and for forcing notions with the (...)
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  4.  19
    Forcing the Mapping Reflection Principle by finite approximations.Tadatoshi Miyamoto & Teruyuki Yorioka - 2021 - Archive for Mathematical Logic 60 (6):737-748.
    Moore introduced the Mapping Reflection Principle and proved that the Bounded Proper Forcing Axiom implies that the size of the continuum is ℵ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\aleph _2$$\end{document}. The Mapping Reflection Principle follows from the Proper Forcing Axiom. To show this, Moore utilized forcing notions whose conditions are countable objects. Chodounský–Zapletal introduced the Y-Proper Forcing Axiom that is a weak fragments of the Proper Forcing Axiom but implies some important conclusions from the Proper Forcing Axiom, (...)
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  5. Some weak fragments of Martin’s axiom related to the rectangle refining property.Teruyuki Yorioka - 2008 - Archive for Mathematical Logic 47 (1):79-90.
    We introduce the anti-rectangle refining property for forcing notions and investigate fragments of Martin’s axiom for ℵ1 dense sets related to the anti-rectangle refining property, which is close to some fragment of Martin’s axiom for ℵ1 dense sets related to the rectangle refining property, and prove that they are really weaker fragments.
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  6.  81
    A correction to “A non-implication between fragments of Martin’s Axiom related to a property which comes from Aronszajn trees”.Teruyuki Yorioka - 2011 - Annals of Pure and Applied Logic 162 (9):752-754.
    In the paper A non-implication between fragments of Martin’s Axiom related to a property which comes from Aronszajn trees , Proposition 2.7 is not true. To avoid this error and correct Proposition 2.7, the definition of the property is changed. In Yorioka [1], all proofs of lemmas and theorems but Lemma 6.9 are valid about this definition without changing the proofs. We give a new statement and a new proof of Lemma 6.9.
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  7.  39
    Forcings with the countable chain condition and the covering number of the Marczewski ideal.Teruyuki Yorioka - 2003 - Archive for Mathematical Logic 42 (7):695-710.
    We prove that the covering number of the Marczewski ideal is equal to ℵ1 in the extension with the iteration of Hechler forcing.
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  8.  27
    Asperó–Mota Iteration and the Size of the Continuum.Teruyuki Yorioka - 2023 - Journal of Symbolic Logic 88 (4):1387-1420.
    In this paper we build an Asperó–Mota iteration of length $\omega _2$ that adds a family of $\aleph _2$ many club subsets of $\omega _1$ which cannot be diagonalized while preserving $\aleph _2$. This result discloses a technical limitation of some types of Asperó–Mota iterations.
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  9.  20
    A note on a forcing related to the S‐space problem in the extension with a coherent Suslin tree.Teruyuki Yorioka - 2015 - Mathematical Logic Quarterly 61 (3):169-178.
    One of the main problems about is that whether a coherent Suslin tree forces that there are no S‐spaces under. We analyze a forcing notion related to this problem, and show that under, S forces that every topology on ω1 generated by a basis in the ground model is not an S‐topology. This supplements the previous work due to Stevo Todorčević [25].
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  10.  21
    Club-Isomorphisms of Aronszajn Trees in the Extension with a Suslin Tree.Teruyuki Yorioka - 2017 - Notre Dame Journal of Formal Logic 58 (3):381-396.
    We show that, under PFA, a coherent Suslin tree forces that every two Aronszajn trees are club-isomorphic.
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  11.  15
    Forcing Axioms and Ω-logic.Teruyuki Yorioka - 2009 - Journal of the Japan Association for Philosophy of Science 36 (2):45-52.
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  12.  15
    ℙmax variations related to slaloms.Teruyuki Yorioka - 2006 - Mathematical Logic Quarterly 52 (2):203-216.
    We prove the iteration lemmata, which are the key lemmata to show that extensions by Pmax variations satisfy absoluteness for Π2-statements in the structure 〈H , ∈, NSω 1, R 〉 for some set R of reals in L , for the following statements: The cofinality of the null ideal is ℵ1. There exists a good basis of the strong measure zero ideal.
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  13.  35
    The diamond principle for the uniformity of the meager ideal implies the existence of a destructible gap.Teruyuki Yorioka - 2005 - Archive for Mathematical Logic 44 (6):677-683.
    We prove the theorem from the title which answers a question addressed in the paper of Moore-Hrusak-Dzamonja [3].
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  14.  26
    Distinguishing types of gaps in.Teruyuki Yorioka - 2003 - Journal of Symbolic Logic 68 (4):1261-1276.
    Supplementing the well known results of Kunen we show that Martin’s Axiom is not sufficient to decide the existence of -gaps when -gaps exist, that is, it is consistent with ZFC that Martin’s Axiom holds and there are -gaps but no -gaps.
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