Switch to: References

Add citations

You must login to add citations.
  1. Canonical functions, non-regular ultrafilters and Ulam’s problem on ω1.Oliver Deiser & Dieter Donder - 2003 - Journal of Symbolic Logic 68 (3):713-739.
    Our main results are:Theorem 1. Con implies Con. [In fact equiconsistency holds.]Theorem 3. Con implies Con.Theorem 5. Con ”) implies Con.We start with a discussion of the canonical functions and look at some combinatorial principles. Assuming the domination property of Theorem 1, we use the Ketonen diagram to show that ω2V is a limit of measurable cardinals in Jensen’s core model KMO for measures of order zero. Using related arguments we show that ω2V is a stationary limit of measurable cardinals (...)
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  • Forcing Axioms and the Definability of the Nonstationary Ideal on the First Uncountable.Stefan Hoffelner, Paul Larson, Ralf Schindler & W. U. Liuzhen - forthcoming - Journal of Symbolic Logic:1-18.
    We show that under $\mathsf {BMM}$ and “there exists a Woodin cardinal, $"$ the nonstationary ideal on $\omega _1$ cannot be defined by a $\Pi _1$ formula with parameter $A \subset \omega _1$. We show that the same conclusion holds under the assumption of Woodin’s $(\ast )$ -axiom. We further show that there are universes where $\mathsf {BPFA}$ holds and $\text {NS}_{\omega _1}$ is $\Pi _1(\{\omega _1\})$ -definable. Lastly we show that if the canonical inner model with one Woodin cardinal (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • More on regular and decomposable ultrafilters in ZFC.Paolo Lipparini - 2010 - Mathematical Logic Quarterly 56 (4):340-374.
    We prove, in ZFC alone, some new results on regularity and decomposability of ultrafilters; among them: If m ≥ 1 and the ultrafilter D is , equation imagem)-regular, then D is κ -decomposable for some κ with λ ≤ κ ≤ 2λ ). If λ is a strong limit cardinal and D is , equation imagem)-regular, then either D is -regular or there are arbitrarily large κ < λ for which D is κ -decomposable ). Suppose that λ is singular, (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Distributive ideals and partition relations.C. A. Johnson - 1986 - Journal of Symbolic Logic 51 (3):617-625.
    It is a theorem of Rowbottom [12] that ifκis measurable andIis a normal prime ideal onκ, then for eachλ<κ,In this paper a natural structural property of ideals, distributivity, is considered and shown to be related to this and other ideal theoretic partition relations.The set theoretical terminology is standard and background results on the theory of ideals may be found in [5] and [8]. Throughoutκwill denote an uncountable regular cardinal, andIa proper, nonprincipal,κ-complete ideal onκ.NSκis the ideal of nonstationary subsets ofκ, andIκ= (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations