Switch to: References

Add citations

You must login to add citations.
  1. The covering number of the strong measure zero ideal can be above almost everything else.Miguel A. Cardona, Diego A. Mejía & Ismael E. Rivera-Madrid - 2022 - Archive for Mathematical Logic 61 (5):599-610.
    We show that certain type of tree forcings, including Sacks forcing, increases the covering of the strong measure zero ideal \. As a consequence, in Sacks model, such covering number is equal to the size of the continuum, which indicates that this covering number is consistently larger than any other classical cardinal invariant of the continuum. Even more, Sacks forcing can be used to force that \<\mathrm {cov}<\mathrm {cof}\), which is the first consistency result where more than two cardinal invariants (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Cichoń’s diagram and localisation cardinals.Martin Goldstern & Lukas Daniel Klausner - 2020 - Archive for Mathematical Logic 60 (3):343-411.
    We reimplement the creature forcing construction used by Fischer et al. :1045–1103, 2017. https://doi.org/10.1007/S00153-017-0553-8. arXiv:1402.0367 [math.LO]) to separate Cichoń’s diagram into five cardinals as a countable support product. Using the fact that it is of countable support, we augment our construction by adding uncountably many additional cardinal characteristics, sometimes referred to as localisation cardinals.
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Cofinalities of Borel ideals.Michael Hrušák, Diego Rojas-Rebolledo & Jindřich Zapletal - 2014 - Mathematical Logic Quarterly 60 (1-2):31-39.
    We study the possible values of the cofinality invariant for various Borel ideals on the natural numbers. We introduce the notions of a fragmented and gradually fragmented ideal and prove a dichotomy for fragmented ideals. We show that every gradually fragmented ideal has cofinality consistently strictly smaller than the cardinal invariant and produce a model where there are uncountably many pairwise distinct cofinalities of gradually fragmented ideals.
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Strongly meager and strong measure zero sets.Tomek Bartoszyński & Saharon Shelah - 2002 - Archive for Mathematical Logic 41 (3):245-250.
    In this paper we present two consistency results concerning the existence of large strong measure zero and strongly meager sets. RID=""ID="" Mathematics Subject Classification (2000): 03e35 RID=""ID="" The first author was supported by Alexander von Humboldt Foundation and NSF grant DMS 95-05375. The second author was partially supported by Basic Research Fund, Israel Academy of Sciences, publication 658.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Decisive creatures and large continuum.Jakob Kellner & Saharon Shelah - 2009 - Journal of Symbolic Logic 74 (1):73-104.
    For f, g $ \in \omega ^\omega $ let $c_{f,g}^\forall $ be the minimal number of uniform g-splitting trees (or: Slaloms) to cover the uniform f-splitting tree, i.e., for every branch v of the f-tree, one of the g-trees contains v. $c_{f,g}^\exists $ is the dual notion: For every branch v, one of the g-trees guesses v(m) infinitely often. It is consistent that $c_{f \in ,g \in }^\exists = c_{f \in ,g \in }^\forall = k_ \in $ for N₁ many (...)
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  • Localizations of infinite subsets of $\omega$.Andrzej Rosłanowski & Saharon Shelah - 1996 - Archive for Mathematical Logic 35 (5-6):315-339.
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Many different covering numbers of Yorioka’s ideals.Noboru Osuga & Shizuo Kamo - 2014 - Archive for Mathematical Logic 53 (1-2):43-56.
    For ${b \in {^{\omega}}{\omega}}$ , let ${\mathfrak{c}^{\exists}_{b, 1}}$ be the minimal number of functions (or slaloms with width 1) to catch every functions below b in infinitely many positions. In this paper, by using the technique of forcing, we construct a generic model in which there are many coefficients ${\mathfrak{c}^{\exists}_{{b_\alpha}, 1}}$ with pairwise different values. In particular, under the assumption that a weakly inaccessible cardinal exists, we can construct a generic model in which there are continuum many coefficients ${\mathfrak{c}^{\exists}_{{b_\alpha}, 1}}$ (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Even more simple cardinal invariants.Jakob Kellner - 2008 - Archive for Mathematical Logic 47 (5):503-515.
    Using GCH, we force the following: There are continuum many simple cardinal characteristics with pairwise different values.
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Creature forcing and large continuum: the joy of halving.Jakob Kellner & Saharon Shelah - 2012 - Archive for Mathematical Logic 51 (1-2):49-70.
    For \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${f,g\in\omega^\omega}$$\end{document} let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${c^\forall_{f,g}}$$\end{document} be the minimal number of uniform g-splitting trees needed to cover the uniform f-splitting tree, i.e., for every branch ν of the f-tree, one of the g-trees contains ν. Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${c^\exists_{f,g}}$$\end{document} be the dual notion: For every branch ν, one of the g-trees guesses ν(m) infinitely often. We show that (...)
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • (1 other version)Controlling cardinal characteristics without adding reals.Martin Goldstern, Jakob Kellner, Diego A. Mejía & Saharon Shelah - 2021 - Journal of Mathematical Logic 21 (3):2150018.
    We investigate the behavior of cardinal characteristics of the reals under extensions that do not add new [Formula: see text]-sequences (for some regular [Formula: see text]). As an application, we show that consistently the following cardinal characteristics can be different: The (“independent”) characteristics in Cichoń’s diagram, plus [Formula: see text]. (So we get thirteen different values, including [Formula: see text] and continuum). We also give constructions to alternatively separate other MA-numbers (instead of [Formula: see text]), namely: MA for [Formula: see (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • (1 other version)Controlling cardinal characteristics without adding reals.Martin Goldstern, Jakob Kellner, Diego A. Mejía & Saharon Shelah - 2020 - Journal of Mathematical Logic 21 (3).
    We investigate the behavior of cardinal characteristics of the reals under extensions that do not add new <κ-sequences. As an application, we show that consistently the followi...
    Download  
     
    Export citation  
     
    Bookmark  
  • Continuous Ramsey theory on polish spaces and covering the plane by functions.Stefan Geschke, Martin Goldstern & Menachem Kojman - 2004 - Journal of Mathematical Logic 4 (2):109-145.
    We investigate the Ramsey theory of continuous graph-structures on complete, separable metric spaces and apply the results to the problem of covering a plane by functions. Let the homogeneity number[Formula: see text] of a pair-coloring c:[X]2→2 be the number of c-homogeneous subsets of X needed to cover X. We isolate two continuous pair-colorings on the Cantor space 2ω, c min and c max, which satisfy [Formula: see text] and prove: Theorem. For every Polish space X and every continuous pair-coloringc:[X]2→2with[Formula: see (...)
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  • On cardinal characteristics of Yorioka ideals.Miguel A. Cardona & Diego A. Mejía - 2019 - Mathematical Logic Quarterly 65 (2):170-199.
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Continuum many different things: Localisation, anti-localisation and Yorioka ideals.Miguel A. Cardona, Lukas Daniel Klausner & Diego A. Mejía - 2024 - Annals of Pure and Applied Logic 175 (7):103453.
    Download  
     
    Export citation  
     
    Bookmark  
  • Evasion and prediction.Jörg Brendle & Saharon Shelah - 2003 - Archive for Mathematical Logic 42 (4):349-360.
    Say that a function π:n<ω→n (henceforth called a predictor) k-constantly predicts a real xnω if for almost all intervals I of length k, there is iI such that x(i)=π(x↾i). We study the k-constant prediction number vnconst(k), that is, the size of the least family of predictors needed to k-constantly predict all reals, for different values of n and k, and investigate their relationship.
    Download  
     
    Export citation  
     
    Bookmark  
  • Towards Martins minimum.Tomek Bartoszynski & Andrzej Rosłlanowski - 2002 - Archive for Mathematical Logic 41 (1):65-82.
    We show that it is consistent with MA + ¬CH that the Forcing Axiom fails for all forcing notions in the class of ωω–bounding forcing notions with norms of [17].
    Download  
     
    Export citation  
     
    Bookmark