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Justin Tatch Moore [8]Justin Moore [3]Justin Hartley Moore [1]
  1.  4
    Set Mapping Reflection.Justin Tatch Moore - 2005 - Journal of Mathematical Logic 5 (1):87-97.
    In this note we will discuss a new reflection principle which follows from the Proper Forcing Axiom. The immediate purpose will be to prove that the bounded form of the Proper Forcing Axiom implies both that 2ω = ω2 and that [Formula: see text] satisfies the Axiom of Choice. It will also be demonstrated that this reflection principle implies that □ fails for all regular κ > ω1.
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  2.  24
    Baumgartner’s Isomorphism Problem for $$\Aleph _2$$ ℵ 2 -Dense Suborders of $$\Mathbb {R}$$ R.Justin Tatch Moore & Stevo Todorcevic - 2017 - Archive for Mathematical Logic 56 (7-8):1105-1114.
    In this paper we will analyze Baumgartner’s problem asking whether it is consistent that \ and every pair of \-dense subsets of \ are isomorphic as linear orders. The main result is the isolation of a combinatorial principle \\) which is immune to c.c.c. forcing and which in the presence of \ implies that two \-dense sets of reals can be forced to be isomorphic via a c.c.c. poset. Also, it will be shown that it is relatively consistent with ZFC (...)
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  3.  9
    The Proper Forcing Axiom, Prikry Forcing, and the Singular Cardinals Hypothesis.Justin Tatch Moore - 2006 - Annals of Pure and Applied Logic 140 (1):128-132.
    The purpose of this paper is to present some results which suggest that the Singular Cardinals Hypothesis follows from the Proper Forcing Axiom. What will be proved is that a form of simultaneous reflection follows from the Set Mapping Reflection Principle, a consequence of PFA. While the results fall short of showing that MRP implies SCH, it will be shown that MRP implies that if SCH fails first at κ then every stationary subset of reflects. It will also be demonstrated (...)
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  4.  17
    A Gδ Ideal of Compact Sets Strictly Above the Nowhere Dense Ideal in the Tukey Order.Justin Tatch Moore & Sławomir Solecki - 2008 - Annals of Pure and Applied Logic 156 (2):270-273.
    We prove that there is a -ideal of compact sets which is strictly above in the Tukey order. Here is the collection of all compact nowhere dense subsets of the Cantor set. This answers a question of Louveau and Veličković asked in [Alain Louveau, Boban Veličković, Analytic ideals and cofinal types, Ann. Pure Appl. Logic 99 171–195].
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  5.  23
    Proper Forcing, Cardinal Arithmetic, and Uncountable Linear Orders.Justin Tatch Moore - 2005 - Bulletin of Symbolic Logic 11 (1):51-60.
    In this paper I will communicate some new consequences of the Proper Forcing Axiom. First, the Bounded Proper Forcing Axiom implies that there is a well ordering of R which is Σ 1 -definable in (H(ω 2 ), ∈). Second, the Proper Forcing Axiom implies that the class of uncountable linear orders has a five element basis. The elements are X, ω 1 , ω 1 * , C, C * where X is any suborder of the reals of size (...)
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  6.  10
    Weak Diamond and Open Colorings.Justin Tatch Moore - 2003 - Journal of Mathematical Logic 3 (01):119-125.
    The purpose of this article is to prove the relative consistency of certain statements about open colorings with 2ℵ0 < 2ℵ1. In particular both OCA and the statement that every 1–1 function of size ℵ1 is σ-monotonic are consistent with 2ℵ0 < 2ℵ1. As a corollary we have that 2ℵ0 < 2ℵ1 does not admit a ℙ max variation.
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  7.  11
    Montréal, Québec, Canada May 17–21, 2006.Jeremy Avigad, Sy Friedman, Akihiro Kanamori, Elisabeth Bouscaren, Philip Kremer, Claude Laflamme, Antonio Montalbán, Justin Moore & Helmut Schwichtenberg - 2007 - Bulletin of Symbolic Logic 13 (1).
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  8.  15
    Aronszajn Lines and the Club Filter.Justin Tatch Moore - 2008 - Journal of Symbolic Logic 73 (3):1029-1035.
    The purpose of this note is to demonstrate that a weak form of club guessing on ω1 implies the existence of an Aronszajn line with no Countryman suborders. An immediate consequence is that the existence of a five element basis for the uncountable linear orders does not follow from the forcing axiom for ω-proper forcings.
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  9.  9
    University of California at Berkeley Berkeley, CA, USA March 24–27, 2011.G. Aldo Antonelli, Laurent Bienvenu, Lou van den Dries, Deirdre Haskell, Justin Moore, Christian Rosendal Uic, Neil Thapen & Simon Thomas - 2012 - Bulletin of Symbolic Logic 18 (2).
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  10.  7
    Erratum: "Set Mapping Reflection".Justin Tatch Moore - 2005 - Journal of Mathematical Logic 5 (02):299-299.
  11.  1
    Metrical Analysis of the Pāli Iti-Vuttaka, a Collection of Discourses of BuddhaMetrical Analysis of the Pali Iti-Vuttaka, a Collection of Discourses of Buddha.Justin Hartley Moore - 1907 - Journal of the American Oriental Society 28:317.
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  12. Stevo Todorcevic. Walks on Ordinals and Their Characteristics. Progress in Mathematics, Vol. 263. Birkhäuser Verlag, Basel, 2007, Vi + 324 Pp. [REVIEW]Justin Moore - 2011 - Bulletin of Symbolic Logic 17 (1):118-119.