6 found
Order:
  1.  5
    Kurepa Trees and Namba Forcing.Bernhard König & Yasuo Yoshinobu - 2012 - Journal of Symbolic Logic 77 (4):1281-1290.
    We show that strongly compact cardinals and MM are sensitive to $\lambda$-closed forcings for arbitrarily large $\lambda$. This is done by adding ‘regressive' $\lambda$-Kurepa trees in either case. We argue that the destruction of regressive Kurepa trees requires a non-standard application of MM. As a corollary, we find a consistent example of an $\omega_2$-closed poset that is not forcing equivalent to any $\omega_2$-directed-closed poset.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  2.  5
    Forcing Indestructibility of Set-Theoretic Axioms.Bernhard König - 2007 - Journal of Symbolic Logic 72 (1):349 - 360.
    Various theorems for the preservation of set-theoretic axioms under forcing are proved, regarding both forcing axioms and axioms true in the Lévy collapse. These show in particular that certain applications of forcing axioms require to add generic countable sequences high up in the set-theoretic hierarchy even before collapsing everything down to ‮א‬₁. Later we give applications, among them the consistency of MM with ‮א‬ω not being Jónsson which answers a question raised in the set theory meeting at Oberwolfach in 2005.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  3.  1
    Local Coherence.Bernhard König - 2003 - Annals of Pure and Applied Logic 124 (1-3):107-139.
    We characterize the tree of functions with finite support in terms of definability. This turns out to have various applications: a new kind of tree dichotomy for ω1 on the one hand. On the other hand, we prove a reflection principle for trees on ω2 under SPFA. This reflection of trees implies stationary reflection.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  4.  9
    Generic Compactness Reformulated.Bernhard König - 2004 - Archive for Mathematical Logic 43 (3):311-326.
    We point out a connection between reflection principles and generic large cardinals. One principle of pure reflection is introduced that is as strong as generic supercompactness of ω2 by Σ-closed forcing. This new concept implies CH and extends the reflection principles for stationary sets in a canonical way.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography  
  5.  8
    Dense Subtrees in Complete Boolean Algebras.Bernhard König - 2006 - Mathematical Logic Quarterly 52 (3):283-287.
    We characterize complete Boolean algebras with dense subtrees. The main results show that a complete Boolean algebra contains a dense tree if its generic filter collapses the algebra's density to its distributivity number and the reverse holds for homogeneous algebras.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  6.  2
    Winning Strategies in Club Games and Their Applications.Bernhard König - 2011 - Mathematical Logic Quarterly 57 (1):19-26.
    We present results concerning winning strategies and tactics in club games on [MATHEMATICAL SCRIPT CAPITAL P]math imageλ. We show that there is generally no winning tactic for the player trying to get inside the club. The bound-countable game turns out to be rather fruitful and adds to some previous results about the construction of elementary substructures and their localization in certain intervals. We show that Player II has a winning strategy in the bound-countable game, thus establishing a new ZFC result. (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography