26 found
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  1.  16
    Sacks Forcing, Laver Forcing, and Martin's Axiom.Haim Judah, Arnold W. Miller & Saharon Shelah - 1992 - Archive for Mathematical Logic 31 (3):145-161.
    In this paper we study the question assuming MA+⌝CH does Sacks forcing or Laver forcing collapse cardinals? We show that this question is equivalent to the question of what is the additivity of Marczewski's ideals 0. We give a proof that it is consistent that Sacks forcing collapses cardinals. On the other hand we show that Laver forcing does not collapse cardinals.
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  2. ▵13-Sets of Reals.Haim Judah & Saharon Shelah - 1993 - Journal of Symbolic Logic 58 (1):72 - 80.
    We build models where all $\underset{\sim}{\triangle}^1_3$ -sets of reals are measurable and (or) have the property of Baire and (or) are Ramsey. We will show that there is no implication between any of these properties for $\underset{\sim}{\triangle}^1_3$ -sets of reals.
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  3.  19
    The Kunen-Miller Chart (Lebesgue Measure, the Baire Property, Laver Reals and Preservation Theorems for Forcing).Haim Judah & Saharon Shelah - 1990 - Journal of Symbolic Logic 55 (3):909-927.
    In this work we give a complete answer as to the possible implications between some natural properties of Lebesgue measure and the Baire property. For this we prove general preservation theorems for forcing notions. Thus we answer a decade-old problem of J. Baumgartner and answer the last three open questions of the Kunen-Miller chart about measure and category. Explicitly, in \S1: (i) We prove that if we add a Laver real, then the old reals have outer measure one. (ii) We (...)
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  4.  6
    Combinatorial Properties of Hechler Forcing.Jörg Brendle, Haim Judah & Saharon Shelah - 1992 - Annals of Pure and Applied Logic 58 (3):185-199.
    Brendle, J., H. Judah and S. Shelah, Combinatorial properties of Hechler forcing, Annals of Pure and Applied Logic 59 185–199. Using a notion of rank for Hechler forcing we show: assuming ωV1 = ωL1, there is no real in V[d] which is eventually different from the reals in L[ d], where d is Hechler over V; adding one Hechler real makes the invariants on the left-hand side of Cichoń's diagram equal ω1 and those on the right-hand side equal 2ω and (...)
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  5. Amoeba Reals.Haim Judah & Miroslav Repickẏ - 1995 - Journal of Symbolic Logic 60 (4):1168-1185.
    We define the ideal with the property that a real omits all Borel sets in the ideal which are coded in a transitive model if and only if it is an amoeba real over this model. We investigate some other properties of this ideal. Strolling through the "amoeba forest" we gain as an application a modification of the proof of the inequality between the additivities of Lebesgue measure and Baire category.
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  6.  34
    The Cichoń Diagram.Tomek Bartoszyński, Haim Judah & Saharon Shelah - 1993 - Journal of Symbolic Logic 58 (2):401 - 423.
    We conclude the discussion of additivity, Baire number, uniformity, and covering for measure and category by constructing the remaining 5 models. Thus we complete the analysis of Cichon's diagram.
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  7.  4
    Exact Equiconsistency Results for Δ 3 1 -Sets of Reals.Haim Judah - 1992 - Archive for Mathematical Logic 32 (2):101-112.
    We improve a theorem of Raisonnier by showing that Cons(ZFC+every Σ 2 1 -set of reals in Lebesgue measurable+every Π 2 1 -set of reals isK σ-regular) implies Cons(ZFC+there exists an inaccessible cardinal). We construct, fromL, a model where every Δ 3 1 -sets of reals is Lebesgue measurable, has the property of Baire, and every Σ 2 1 -set of reals isK σ-regular. We prove that if there exists a Σ n+1 1 unbounded filter on ω, then there exists (...)
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  8.  4
    Jumping with Random Reals.Tomek Bartoszynski & Haim Judah - 1990 - Annals of Pure and Applied Logic 48 (3):197-213.
  9.  8
    Mathias Absoluteness and the Ramsey Property.Lorenz Halbeisen & Haim Judah - 1996 - Journal of Symbolic Logic 61 (1):177-194.
    In this article we give a forcing characterization for the Ramsey property of Σ 1 2 -sets of reals. This research was motivated by the well-known forcing characterizations for Lebesgue measurability and the Baire property of Σ 1 2 -sets of reals. Further we will show the relationship between higher degrees of forcing absoluteness and the Ramsey property of projective sets of reals.
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  10.  45
    Strong Measure Zero Sets Without Cohen Reals.Martin Goldstern, Haim Judah & Saharon Shelah - 1993 - Journal of Symbolic Logic 58 (4):1323-1341.
    If ZFC is consistent, then each of the following is consistent with ZFC + 2ℵ0 = ℵ2: (1) $X \subseteq \mathbb{R}$ is of strong measure zero iff |X| ≤ ℵ1 + there is a generalized Sierpinski set. (2) The union of ℵ1 many strong measure zero sets is a strong measure zero set + there is a strong measure zero set of size ℵ2 + there is no Cohen real over L.
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  11.  3
    The Borel Conjecture.Haim Judah, Saharon Shelah & W. H. Woodin - 1990 - Annals of Pure and Applied Logic 50 (3):255-269.
    We show the Borel Conjecture is consistent with the continuum large.
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  12.  14
    Kelley-Morse+Types of Well Order is Not a Conservative Extension of Kelley Morse.Haim Judah & M. Victoria Marshall - 1994 - Archive for Mathematical Logic 33 (1):13-21.
    Assuming the consistency ofZF + “There is an inaccessible number of inaccessibles”, we prove that Kelley Morse theory plus types is not a conservative extension of Kelley-Morse theory.
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  13.  20
    Martin's Axiom and the Continuum.Haim Judah & Andrzej Rosłanowski - 1995 - Journal of Symbolic Logic 60 (2):374-391.
  14.  7
    -Sets of Reals.Haim Judah & Saharon Shelah - 1993 - Journal of Symbolic Logic 58 (1):72-80.
  15.  7
    Large Cardinals and Projective Sets.Haim Judah & Otmar Spinas - 1997 - Archive for Mathematical Logic 36 (2):137-155.
    We investigate measure and category in the projective hierarchie in the presence of large cardinals. Assuming a measurable larger than $n$ Woodin cardinals we construct a model where every $\Delta ^1_{n+4}$ -set is measurable, but some $\Delta ^1_{n+4}$ -set does not have Baire property. Moreover, from the same assumption plus a precipitous ideal on $\omega _1$ we show how a model can be forced where every $\Sigma ^1_{n+4}-$ set is measurable and has Baire property.
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  16.  10
    Around Random Algebra.Haim Judah & Saharon Shelah - 1990 - Archive for Mathematical Logic 30 (3):129-138.
    It is shown that there is a subalgebra of the measure algebra forcing dominating reals. Also results are given about iterated forcing connected with random reals.
    No categories
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  17.  6
    $Triangle^1_3$-Sets of Reals.Haim Judah & Saharon Shelah - 1993 - Journal of Symbolic Logic 58 (1):72-80.
    We build models where all $\underset{\sim}{\triangle}^1_3$-sets of reals are measurable and (or) have the property of Baire and (or) are Ramsey. We will show that there is no implication between any of these properties for $\underset{\sim}{\triangle}^1_3$-sets of reals.
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  18.  11
    Forcing Minimal Degree of Constructibility.Haim Judah & Saharon Shelah - 1991 - Journal of Symbolic Logic 56 (3):769-782.
    In this paper we will study four forcing notions, two of them giving a minimal degree of constructibility. These constructions give answers to questions in [Ih].
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  19.  4
    On the Structure of [Mathematical Formula]-Sets of Reals.Haim Judah & Otmar Spinas - 1995 - Archive for Mathematical Logic 5.
  20.  3
    Forcing Minimal Degree of Constructibility.Haim Judah & Saharon Shelah - 1991 - Journal of Symbolic Logic 56 (3):769.
    In this paper we will study four forcing notions, two of them giving a minimal degree of constructibility. These constructions give answers to questions in [Ih].
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  21.  24
    ▵13-Stability.Dror Ben-Arie & Haim Judah - 1993 - Journal of Symbolic Logic 58 (3).
  22.  8
    On the Structure of Δ 1 4 -Sets of Reals.Haim Judah & Otmar Spinas - 1995 - Archive for Mathematical Logic 34 (5):301-312.
    Assuming that an inaccessible cardinal exists, we construct a ZFC-model where every Δ 1 4 -set is measurable but there exists a Δ 1 4 -set without the property of Baire. By a result of Shelah, an inaccessible cardinal is necessary for this result.
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  23.  4
    On the Structure of $\Vec{\Delta_4^1}$ -Sets of Reals.Haim Judah & Otmar Spinas - 1995 - Archive for Mathematical Logic 34 (5):301-312.
  24.  2
    -Stability.Dror Ben-Arié & Haim Judah - 1993 - Journal of Symbolic Logic 58 (3):941-954.
  25.  2
    $Triangle^1_3$-Stability.Dror Ben-Arie & Haim Judah - 1993 - Journal of Symbolic Logic 58 (3):941-954.
    We investigate the connection between $\triangle^1_3$-stability for random and Cohen forcing notions and the measurability and categoricity of the $\triangle^1_3$-sets. We show that Shelah's model for $\triangle^1_3$-measurability and categoricity satisfies $\triangle^1_3$-random-stability while it does not satisfy $\triangle^1_3$-Cohen-stability. This gives an example of measure-category asymmetry. We also present a result concerning finite support iterations of Suslin forcing.
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  26. Δ1/3-Sets of Reals.Haim Judah & Saharon Shelah - 1993 - Journal of Symbolic Logic 58 (1):72-80.