Switch to: References

Add citations

You must login to add citations.
  1. Chain conditions of products, and weakly compact cardinals.Assaf Rinot - 2014 - Bulletin of Symbolic Logic 20 (3):293-314,.
    The history of productivity of the κ-chain condition in partial orders, topological spaces, or Boolean algebras is surveyed, and its connection to the set-theoretic notion of a weakly compact cardinal is highlighted. Then, it is proved that for every regular cardinal κ > א1, the principle □ is equivalent to the existence of a certain strong coloring c : [κ]2 → κ for which the family of fibers T is a nonspecial κ-Aronszajn tree. The theorem follows from an analysis of (...)
    Download  
     
    Export citation  
     
    Bookmark   14 citations  
  • Combinatorial principles in the core model for one Woodin cardinal.Ernest Schimmerling - 1995 - Annals of Pure and Applied Logic 74 (2):153-201.
    We study the fine structure of the core model for one Woodin cardinal, building of the work of Mitchell and Steel on inner models of the form . We generalize to some combinatorial principles that were shown by Jensen to hold in L. We show that satisfies the statement: “□κ holds whenever κ the least measurable cardinal λ of order λ++”. We introduce a hierarchy of combinatorial principles □κ, λ for 1 λ κ such that □κ□κ, 1 □κ, λ □κ, (...)
    Download  
     
    Export citation  
     
    Bookmark   49 citations  
  • Hierarchies of forcing axioms I.Itay Neeman & Ernest Schimmerling - 2008 - Journal of Symbolic Logic 73 (1):343-362.
    We prove new upper bound theorems on the consistency strengths of SPFA (θ), SPFA(θ-linked) and SPFA(θ⁺-cc). Our results are in terms of (θ, Γ)-subcompactness, which is a new large cardinal notion that combines the ideas behind subcompactness and Γ-indescribability. Our upper bound for SPFA(c-linked) has a corresponding lower bound, which is due to Neeman and appears in his follow-up to this paper. As a corollary, SPFA(c-linked) and PFA(c-linked) are each equiconsistent with the existence of a $\Sigma _{1}^{2}$ -indescribable cardinal. Our (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Successive cardinals with no partial square.John Krueger - 2014 - Archive for Mathematical Logic 53 (1-2):11-21.
    We construct a model in which for all 1 ≤ n < ω, there is no stationary subset of ${\aleph_{n+1} \cap {\rm cof}(\aleph_n)}$ which carries a partial square.
    Download  
     
    Export citation  
     
    Bookmark  
  • 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.
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • 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.
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Diagonal reflections on squares.Gunter Fuchs - 2019 - Archive for Mathematical Logic 58 (1-2):1-26.
    The effects of the forcing axioms \, \ and \ on the failure of weak threaded square principles of the form \\) are analyzed. To this end, a diagonal reflection principle, \, and it implies the failure of \\) if \. It is also shown that this result is sharp. It is noted that \/\ imply the failure of \\), for every regular \, and that this result is sharp as well.
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Square and Delta reflection.Laura Fontanella & Yair Hayut - 2016 - Annals of Pure and Applied Logic 167 (8):663-683.
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • A microscopic approach to Souslin-tree construction, Part II.Ari Meir Brodsky & Assaf Rinot - 2021 - Annals of Pure and Applied Logic 172 (5):102904.
    In Part I of this series, we presented the microscopic approach to Souslin-tree constructions, and argued that all known ⋄-based constructions of Souslin trees with various additional properties may be rendered as applications of our approach. In this paper, we show that constructions following the same approach may be carried out even in the absence of ⋄. In particular, we obtain a new weak sufficient condition for the existence of Souslin trees at the level of a strongly inaccessible cardinal. We (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • 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.
    Download  
     
    Export citation  
     
    Bookmark   6 citations