12 found
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  1.  29
    Aronszajn Trees and the Successors of a Singular Cardinal.Spencer Unger - 2013 - Archive for Mathematical Logic 52 (5-6):483-496.
    From large cardinals we obtain the consistency of the existence of a singular cardinal κ of cofinality ω at which the Singular Cardinals Hypothesis fails, there is a bad scale at κ and κ ++ has the tree property. In particular this model has no special κ +-trees.
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  2.  47
    Fragility and Indestructibility of the Tree Property.Spencer Unger - 2012 - Archive for Mathematical Logic 51 (5-6):635-645.
    We prove various theorems about the preservation and destruction of the tree property at ω 2. Working in a model of Mitchell [9] where the tree property holds at ω 2, we prove that ω 2 still has the tree property after ccc forcing of size ${\aleph_1}$ or adding an arbitrary number of Cohen reals. We show that there is a relatively mild forcing in this same model which destroys the tree property. Finally we prove from a supercompact cardinal that (...)
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  3.  16
    Fragility and Indestructibility II.Spencer Unger - 2015 - Annals of Pure and Applied Logic 166 (11):1110-1122.
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  4.  15
    The Tree Property Belowℵω⋅2.Spencer Unger - 2016 - Annals of Pure and Applied Logic 167 (3):247-261.
  5.  12
    The Tree Property at And.Dima Sinapova & Spencer Unger - 2018 - Journal of Symbolic Logic 83 (2):669-682.
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  6.  8
    A Model of Cummings and Foreman Revisited.Spencer Unger - 2014 - Annals of Pure and Applied Logic 165 (12):1813-1831.
  7.  6
    Diagonal Supercompact Radin Forcing.Omer Ben-Neria, Chris Lambie-Hanson & Spencer Unger - 2020 - Annals of Pure and Applied Logic 171 (10):102828.
    Motivated by the goal of constructing a model in which there are no κ-Aronszajn trees for any regular $k>\aleph_1$, we produce a model with many singular cardinals where both the singular cardinals hypothesis and weak square fail.
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  8.  10
    Combinatorics Atℵω.Dima Sinapova & Spencer Unger - 2014 - Annals of Pure and Applied Logic 165 (4):996-1007.
    We construct a model in which the singular cardinal hypothesis fails at ℵωℵω. We use characterizations of genericity to show the existence of a projection between different Prikry type forcings.
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  9.  15
    Homogeneous Changes in Cofinalities with Applications to HOD.Omer Ben-Neria & Spencer Unger - 2017 - Journal of Mathematical Logic 17 (2):1750007.
    We present a new technique for changing the cofinality of large cardinals using homogeneous forcing. As an application we show that many singular cardinals in [Formula: see text] can be measurable in HOD. We also answer a related question of Cummings, Friedman and Golshani by producing a model in which every regular uncountable cardinal [Formula: see text] in [Formula: see text] is [Formula: see text]-supercompact in HOD.
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  10. The Tree Property at the Two Immediate Successors of a Singular Cardinal.James Cummings, Yair Hayut, Menachem Magidor, Itay Neeman, Dima Sinapova & Spencer Unger - forthcoming - Journal of Symbolic Logic:1-9.
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  11.  5
    Stationary Reflection.Yair Hayut & Spencer Unger - 2020 - Journal of Symbolic Logic 85 (3):937-959.
    We improve the upper bound for the consistency strength of stationary reflection at successors of singular cardinals.
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  12.  17
    The Strong Tree Property and Weak Square.Yair Hayut & Spencer Unger - 2017 - Mathematical Logic Quarterly 63 (1-2):150-154.
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