Switch to: References

Add citations

You must login to add citations.
  1. Rado’s Conjecture and its Baire version.Jing Zhang - 2019 - Journal of Mathematical Logic 20 (1):1950015.
    Rado’s Conjecture is a compactness/reflection principle that says any nonspecial tree of height ω1 has a nonspecial subtree of size ℵ1. Though incompatible with Martin’s Axiom, Rado’s Conjecture turns out to have many interesting consequences that are also implied by certain forcing axioms. In this paper, we obtain consistency results concerning Rado’s Conjecture and its Baire version. In particular, we show that a fragment of PFA, which is the forcing axiom for Baire Indestructibly Proper forcings, is compatible with the Baire (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Rado's Conjecture and Ascent Paths of Square Sequences.Stevo Todorčević & Víctor Torres Pérez - 2014 - Mathematical Logic Quarterly 60 (1-2):84-90.
    This is a continuation of our paper where we show that Rado's Conjecture can trivialize ‐sequences in some cases when ϑ is not necessarily a successor cardinal.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Chang’s Conjecture and weak square.Hiroshi Sakai - 2013 - Archive for Mathematical Logic 52 (1-2):29-45.
    We investigate how weak square principles are denied by Chang’s Conjecture and its generalizations. Among other things we prove that Chang’s Conjecture does not imply the failure of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square_{\omega_1, 2}}$$\end{document}, i.e. Chang’s Conjecture is consistent with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square_{\omega_1, 2}}$$\end{document}.
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  • Guessing more sets.Pierre Matet - 2015 - Annals of Pure and Applied Logic 166 (10):953-990.
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • Squares, ascent paths, and chain conditions.Chris Lambie-Hanson & Philipp Lücke - 2018 - Journal of Symbolic Logic 83 (4):1512-1538.
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • Aronszajn trees, square principles, and stationary reflection.Chris Lambie-Hanson - 2017 - Mathematical Logic Quarterly 63 (3-4):265-281.
    We investigate questions involving Aronszajn trees, square principles, and stationary reflection. We first consider two strengthenings of introduced by Brodsky and Rinot for the purpose of constructing κ‐Souslin trees. Answering a question of Rinot, we prove that the weaker of these strengthenings is compatible with stationary reflection at κ but the stronger is not. We then prove that, if μ is a singular cardinal, implies the existence of a special ‐tree with a cf(μ)‐ascent path, thus answering a question of Lücke.
    Download  
     
    Export citation  
     
    Bookmark   6 citations