Switch to: References

Add citations

You must login to add citations.
  1. Adding Closed Unbounded Subsets of ω₂ with Finite Forcing.William J. Mitchell - 2005 - Notre Dame Journal of Formal Logic 46 (3):357-371.
    An outline is given of the proof that the consistency of a κ⁺-Mahlo cardinal implies that of the statement that I[ω₂] does not include any stationary subsets of Cof(ω₁). An additional discussion of the techniques of this proof includes their use to obtain a model with no ω₂-Aronszajn tree and to add an ω₂-Souslin tree with finite conditions.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   12 citations  
  • Guessing models and the approachability ideal.Rahman Mohammadpour & Boban Veličković - 2020 - Journal of Mathematical Logic 21 (2):2150003.
    Starting with two supercompact cardinals we produce a generic extension of the universe in which a principle that we call GM+ holds. This principle implies ISP and ISP, and hence th...
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • On the Hamkins approximation property.William J. Mitchell - 2006 - Annals of Pure and Applied Logic 144 (1-3):126-129.
    We give a short proof of a lemma which generalizes both the main lemma from the original construction in the author’s thesis of a model with no ω2-Aronszajn trees, and also the “Key Lemma” in Hamkins’ gap forcing theorems. The new lemma directly yields Hamkins’ newer lemma stating that certain forcing notions have the approximation property.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   15 citations  
  • Separating weak partial square principles.John Krueger & Ernest Schimmerling - 2014 - Annals of Pure and Applied Logic 165 (2):609-619.
    We introduce the weak partial square principles View the MathML source and View the MathML source, which combine the ideas of a weak square sequence and a partial square sequence. We construct models in which weak partial square principles fail. The main result of the paper is that □λ,κ does not imply View the MathML source.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • An equiconsistency result on partial squares.John Krueger & Ernest Schimmerling - 2011 - Journal of Mathematical Logic 11 (1):29-59.
    We prove that the following two statements are equiconsistent: there exists a greatly Mahlo cardinal; there exists a regular uncountable cardinal κ such that no stationary subset of κ+ ∩ cof carries a partial square.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   4 citations