9 found
Order:
  1.  25
    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.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  2.  41
    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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  3.  14
    Fragility and Indestructibility II.Spencer Unger - 2015 - Annals of Pure and Applied Logic 166 (11):1110-1122.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  4.  11
    The Tree Property at And.Dima Sinapova & Spencer Unger - 2018 - Journal of Symbolic Logic 83 (2):669-682.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  5.  8
    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.
    Direct download (3 more)  
    Translate
     
     
    Export citation  
     
    Bookmark   4 citations  
  6.  7
    A Model of Cummings and Foreman Revisited.Spencer Unger - 2014 - Annals of Pure and Applied Logic 165 (12):1813-1831.
  7.  14
    The Tree Property Belowℵω⋅2.Spencer Unger - 2016 - Annals of Pure and Applied Logic 167 (3):247-261.
  8.  14
    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.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  9.  16
    The Strong Tree Property and Weak Square.Yair Hayut & Spencer Unger - 2017 - Mathematical Logic Quarterly 63 (1-2):150-154.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark