13 found
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  1.  43
    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.  53
    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 ω2. Working in a model of Mitchell [9] where the tree property holds at ω2, we prove that ω2 still has the tree property after ccc forcing of size \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\aleph_1}$$\end{document} 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 (...)
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  3.  17
    Stationary Reflection and the Failure of the Sch.Omer Ben-Neria, Yair Hayut & Spencer Unger - 2024 - Journal of Symbolic Logic 89 (1):1-26.
    In this paper we prove that from large cardinals it is consistent that there is a singular strong limit cardinal $\nu $ such that the singular cardinal hypothesis fails at $\nu $ and every collection of fewer than $\operatorname {\mathrm {cf}}(\nu )$ stationary subsets of $\nu ^{+}$ reflects simultaneously. For $\operatorname {\mathrm {cf}}(\nu )> \omega $, this situation was not previously known to be consistent. Using different methods, we reduce the upper bound on the consistency strength of this situation for (...)
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  4.  26
    Fragility and indestructibility II.Spencer Unger - 2015 - Annals of Pure and Applied Logic 166 (11):1110-1122.
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  5.  37
    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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  6.  25
    A model of Cummings and Foreman revisited.Spencer Unger - 2014 - Annals of Pure and Applied Logic 165 (12):1813-1831.
  7.  16
    The tree property at and.Dima Sinapova & Spencer Unger - 2018 - Journal of Symbolic Logic 83 (2):669-682.
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  8.  29
    The tree property below ℵ ω ⋅ 2.Spencer Unger - 2016 - Annals of Pure and Applied Logic 167 (3):247-261.
  9.  22
    Combinatorics at ℵ ω.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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  10.  21
    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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  11.  22
    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.  11
    The tree property at the two immediate successors of a singular cardinal.James Cummings, Yair Hayut, Menachem Magidor, Itay Neeman, Dima Sinapova & Spencer Unger - 2021 - Journal of Symbolic Logic 86 (2):600-608.
    We present an alternative proof that from large cardinals, we can force the tree property at $\kappa ^+$ and $\kappa ^{++}$ simultaneously for a singular strong limit cardinal $\kappa $. The advantage of our method is that the proof of the tree property at the double successor is simpler than in the existing literature. This new approach also works to establish the result for $\kappa =\aleph _{\omega ^2}$.
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  13.  26
    The strong tree property and weak square.Yair Hayut & Spencer Unger - 2017 - Mathematical Logic Quarterly 63 (1-2):150-154.
    We show that it is consistent, relative to ω many supercompact cardinals, that the super tree property holds at for all but there are weak square and a very good scale at.
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