14 found
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  1.  21
    Aronszajn trees on ℵ2 and ℵ3.Uri Abraham - 1983 - Annals of Mathematical Logic 24 (3):213-230.
    Assuming the existence of a supercompact cardinal and a weakly compact cardinal above it, we provide a generic extension where there are no Aronszajn trees of height ω 2 or ω 3 . On the other hand we show that some large cardinal assumptions are necessary for such a consistency result.
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  2.  20
    On the Consistency of Some Partition Theorems for Continuous Colorings, and the Structure of ℵ 1 -Dense Real Order Types.J. Steprans, Uri Abraham, Matatyahu Rubin & Saharon Shelah - 2002 - Bulletin of Symbolic Logic 8 (2):303.
    We present some techniques in c.c.c. forcing, and apply them to prove consistency results concerning the isomorphism and embeddability relations on the family of ℵ 1 -dense sets of real numbers. In this direction we continue the work of Baumgartner [2] who proved the axiom BA stating that every two ℵ 1 -dense subsets of R are isomorphic, is consistent. We e.g. prove Con). Let K H , be the set of order types of ℵ 1 -dense homogeneous subsets of (...)
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  3.  52
    Forcing closed unbounded sets.Uri Abraham & Saharon Shelah - 1983 - Journal of Symbolic Logic 48 (3):643-657.
    We discuss the problem of finding forcing posets which introduce closed unbounded subsets to a given stationary set.
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  4.  23
    A Δ22 well-order of the reals and incompactness of L.Uri Abraham & Saharon Shelah - 1993 - Annals of Pure and Applied Logic 59 (1):1-32.
    A forcing poset of size 221 which adds no new reals is described and shown to provide a Δ22 definable well-order of the reals . The encoding of this well-order is obtained by playing with products of Aronszajn trees: some products are special while other are Suslin trees. The paper also deals with the Magidor–Malitz logic: it is consistent that this logic is highly noncompact.
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  5.  15
    A Δ< sup> 2< sub> 2 well-order of the reals and incompactness of< i> L(< i> QMM).Uri Abraham & Saharon Shelah - 1993 - Annals of Pure and Applied Logic 59 (1):1-32.
  6.  76
    Coding with ladders a well ordering of the reals.Uri Abraham & Saharon Shelah - 2002 - Journal of Symbolic Logic 67 (2):579-597.
    Any model of ZFC + GCH has a generic extension (made with a poset of size ℵ 2 ) in which the following hold: MA + 2 ℵ 0 = ℵ 2 +there exists a Δ 2 1 -well ordering of the reals. The proof consists in iterating posets designed to change at will the guessing properties of ladder systems on ω 1 . Therefore, the study of such ladders is a main concern of this article.
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  7.  35
    Some Results in Polychromatic Ramsey Theory.Uri Abraham, James Cummings & Clifford Smyth - 2007 - Journal of Symbolic Logic 72 (3):865 - 896.
  8.  37
    Ladder Gaps over Stationary Sets.Uri Abraham & Saharon Shelah - 2004 - Journal of Symbolic Logic 69 (2):518 - 532.
    For a stationary set $S \subseteq \omega_{1}$ and a ladder system C over S, a new type of gaps called C-Hausdorff is introduced and investigated. We describe a forcing model of ZFC in which, for some stationary set S, for every ladder C over S, every gap contains a subgap that is C-Hausdorff. But for every ladder E over \omega_{1} \ S$ there exists a gap with no subgap that is E-Hausdorff. A new type of chain condition, called polarized chain (...)
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  9.  19
    Preface.Uri Abraham, Lev Beklemishev, Paola D'Aquino & Marcus Tressl - 2016 - Annals of Pure and Applied Logic 167 (10):865-867.
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  10.  12
    2010 european summer meeting of the association for symbolic logic logic colloquium'10.Uri Abraham & Ted Slaman - 2011 - Bulletin of Symbolic Logic 17 (2):272-329.
  11.  40
    Martin's axiom and well-ordering of the reals.Uri Abraham & Saharon Shelah - 1996 - Archive for Mathematical Logic 35 (5):287-298.
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  12.  8
    Free Sets for Commutative Families of Functions.Uri Abraham - 1989 - In Jens Erik Fenstad, Ivan Timofeevich Frolov & Risto Hilpinen (eds.), Logic, Methodology, and Philosophy of Science Viii: Proceedings of the Eighth International Congress of Logic, Methodology, and Philosophy of Science, Moscow, 1987. Sole Distributors for the U.S.A. And Canada, Elsevier Science.
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  13.  49
    On forcing without the continuum hypothesis.Uri Abraham - 1983 - Journal of Symbolic Logic 48 (3):658-661.
  14.  24
    Martin's axiom and $\Delta^2_1$ well-ordering of the reals.Uri Abraham & Saharon Shelah - 1996 - Archive for Mathematical Logic 35 (5-6):287-298.
    Assuming an inaccessible cardinal $\kappa$ , there is a generic extension in which $MA + 2^{\aleph_0} = \kappa$ holds and the reals have a $\Delta^2_1$ well-ordering.
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