Switch to: References

Add citations

You must login to add citations.
  1. A Lifting Argument for the Generalized Grigorieff Forcing.Radek Honzík & Jonathan Verner - 2016 - Notre Dame Journal of Formal Logic 57 (2):221-231.
    In this short paper, we describe another class of forcing notions which preserve measurability of a large cardinal $\kappa$ from the optimal hypothesis, while adding new unbounded subsets to $\kappa$. In some ways these forcings are closer to the Cohen-type forcings—we show that they are not minimal—but, they share some properties with treelike forcings. We show that they admit fusion-type arguments which allow for a uniform lifting argument.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Regularity properties on the generalized reals.Sy David Friedman, Yurii Khomskii & Vadim Kulikov - 2016 - Annals of Pure and Applied Logic 167 (4):408-430.
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  • Perfect tree forcings for singular cardinals.Natasha Dobrinen, Dan Hathaway & Karel Prikry - 2020 - Annals of Pure and Applied Logic 171 (9):102827.
    Download  
     
    Export citation  
     
    Bookmark  
  • Grigorieff Forcing on Uncountable Cardinals Does Not Add a Generic of Minimal Degree.Brooke M. Andersen & Marcia J. Groszek - 2009 - Notre Dame Journal of Formal Logic 50 (2):195-200.
    Grigorieff showed that forcing to add a subset of ω using partial functions with suitably chosen domains can add a generic real of minimal degree. We show that forcing with partial functions to add a subset of an uncountable κ without adding a real never adds a generic of minimal degree. This is in contrast to forcing using branching conditions, as shown by Brown and Groszek.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • More about λ-support iterations of (<λ)-complete forcing notions.Andrzej Rosłanowski & Saharon Shelah - 2013 - Archive for Mathematical Logic 52 (5-6):603-629.
    This article continues Rosłanowski and Shelah (Int J Math Math Sci 28:63–82, 2001; Quaderni di Matematica 17:195–239, 2006; Israel J Math 159:109–174, 2007; 2011; Notre Dame J Formal Logic 52:113–147, 2011) and we introduce here a new property of (<λ)-strategically complete forcing notions which implies that their λ-support iterations do not collapse λ + (for a strongly inaccessible cardinal λ).
    Download  
     
    Export citation  
     
    Bookmark   4 citations