11 found
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  1.  26
    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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  2.  94
    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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  3.  61
    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.  16
    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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  5.  63
    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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  6.  34
    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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  7.  20
    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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  8.  4
    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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  9.  5
    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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  10.  5
    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.
  11.  3
    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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