Switch to: References

Add citations

You must login to add citations.
  1. < I> P_-Points in Qmax Models.Qi Feng & W. Hugh Woodin - 2003 - Annals of Pure and Applied Logic 119 (1):121-190.
  • ℙmax Variations for Separating Club Guessing Principles.Tetsuya Ishiu & Paul B. Larson - 2012 - Journal of Symbolic Logic 77 (2):532-544.
    In his book on P max [7], Woodin presents a collection of partial orders whose extensions satisfy strong club guessing principles on ω | . In this paper we employ one of the techniques from this book to produce P max variations which separate various club guessing principles. The principle (+) and its variants are weak guessing principles which were first considered by the second author [4] while studying games of length ω | . It was shown in [1] that (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark  
  • Terminal Notions in Set Theory.Jindřich Zapletal - 2001 - Annals of Pure and Applied Logic 109 (1-2):89-116.
    In mathematical practice certain formulas φ are believed to essentially decide all other natural properties of the object x. The purpose of this paper is to exactly quantify such a belief for four formulas φ, namely “x is a Ramsey ultrafilter”, “x is a free Souslin tree”, “x is an extendible strong Lusin set” and “x is a good diamond sequence”.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  • P-Points in Qmax Models.Q. Feng & W. H. Woodin - 2003 - Annals of Pure and Applied Logic 119 (1-3):121-190.
    We show how to get canonical models from in which the nonstationary ideal on ω1 is ω1 dense and there is no P-point.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • 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 (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • A Microscopic Approach to Souslin-Tree Constructions, Part I.Ari Meir Brodsky & Assaf Rinot - 2017 - Annals of Pure and Applied Logic 168 (11):1949-2007.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • Saturation, Suslin Trees and Meager Sets.Paul Larson - 2005 - Archive for Mathematical Logic 44 (5):581-595.
    We show, using a variation of Woodin’s partial order ℙ max , that it is possible to destroy the saturation of the nonstationary ideal on ω 1 by forcing with a Suslin tree. On the other hand, Suslin trees typcially preserve saturation in extensions by ℙ max variations where one does not try to arrange it otherwise. In the last section, we show that it is possible to have a nonmeager set of reals of size ℵ1, saturation of the nonstationary (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • Souslin Algebra Embeddings.Gido Scharfenberger-Fabian - 2011 - Archive for Mathematical Logic 50 (1-2):75-113.
    A Souslin algebra is a complete Boolean algebra whose main features are ruled by a tight combination of an antichain condition with an infinite distributive law. The present article divides into two parts. In the first part a representation theory for the complete and atomless subalgebras of Souslin algebras is established (building on ideas of Jech and Jensen). With this we obtain some basic results on the possible types of subalgebras and their interrelation. The second part begins with a review (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • Forcing Axioms and Ω-Logic.Teruyuki Yorioka - 2009 - Journal of the Japan Association for Philosophy of Science 36 (2):45-52.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  • ℙmax Variations Related to Slaloms.Teruyuki Yorioka - 2006 - Mathematical Logic Quarterly 52 (2):203-216.
    We prove the iteration lemmata, which are the key lemmata to show that extensions by Pmax variations satisfy absoluteness for Π2-statements in the structure 〈H , ∈, NSω 1, R 〉 for some set R of reals in L , for the following statements: The cofinality of the null ideal is ℵ1. There exists a good basis of the strong measure zero ideal.
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark