Switch to: Citations

Add references

You must login to add references.
  1. Creature Forcing and Large Continuum: The Joy of Halving.Jakob Kellner & Saharon Shelah - 2012 - Archive for Mathematical Logic 51 (1-2):49-70.
    For ${f,g\in\omega^\omega}$ let ${c^\forall_{f,g}}$ 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 ${c^\exists_{f,g}}$ be the dual notion: For every branch ν, one of the g-trees guesses ν(m) infinitely often. We show that it is consistent that ${c^\exists_{f_\epsilon,g_\epsilon}{=}c^\forall_{f_\epsilon,g_\epsilon}{=}\kappa_\epsilon}$ for continuum many pairwise different cardinals ${\kappa_\epsilon}$ and suitable pairs ${(f_\epsilon,g_\epsilon)}$ . For the proof we introduce a new mixed-limit creature forcing (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  • Matrix Iterations and Cichon’s Diagram.Diego Alejandro Mejía - 2013 - Archive for Mathematical Logic 52 (3-4):261-278.
    Using matrix iterations of ccc posets, we prove the consistency with ZFC of some cases where the cardinals on the right hand side of Cichon’s diagram take two or three arbitrary values (two regular values, the third one with uncountable cofinality). Also, mixing this with the techniques in J Symb Log 56(3):795–810, 1991, we can prove that it is consistent with ZFC to assign, at the same time, several arbitrary regular values on the left hand side of Cichon’s diagram.
    No categories
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   7 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 ${\mathfrak{c}^{\exists}_{{b_\alpha}, 1}}$ (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  • Many Simple Cardinal Invariants.Martin Goldstern & Saharon Shelah - 1993 - Archive for Mathematical Logic 32 (3):203-221.
  • Template Iterations with Non-Definable Ccc Forcing Notions.Diego A. Mejía - 2015 - Annals of Pure and Applied Logic 166 (11):1071-1109.
  • Creature Forcing and Five Cardinal Characteristics in Cichoń’s Diagram.Arthur Fischer, Martin Goldstern, Jakob Kellner & Saharon Shelah - 2017 - Archive for Mathematical Logic 56 (7-8):1045-1103.
    We use a creature construction to show that consistently $$\begin{aligned} \mathfrak d=\aleph _1= {{\mathrm{cov}}}< {{\mathrm{non}}}< {{\mathrm{non}}}< {{\mathrm{cof}}} < 2^{\aleph _0}. \end{aligned}$$The same method shows the consistency of $$\begin{aligned} \mathfrak d=\aleph _1= {{\mathrm{cov}}}< {{\mathrm{non}}}< {{\mathrm{non}}}< {{\mathrm{cof}}} < 2^{\aleph _0}. \end{aligned}$$.
    No categories
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  • Set Theory. An Introduction to Independence Proofs.James E. Baumgartner & Kenneth Kunen - 1986 - Journal of Symbolic Logic 51 (2):462.
  • The Kunen-Miller Chart (Lebesgue Measure, the Baire Property, Laver Reals and Preservation Theorems for Forcing).Haim Judah & Saharon Shelah - 1990 - Journal of Symbolic Logic 55 (3):909-927.
    In this work we give a complete answer as to the possible implications between some natural properties of Lebesgue measure and the Baire property. For this we prove general preservation theorems for forcing notions. Thus we answer a decade-old problem of J. Baumgartner and answer the last three open questions of the Kunen-Miller chart about measure and category. Explicitly, in \S1: (i) We prove that if we add a Laver real, then the old reals have outer measure one. (ii) We (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   15 citations  
  • Adding Dominating Reals with Ωω Bounding Posets.Janusz Pawlikowski - 1992 - Journal of Symbolic Logic 57 (2):540 - 547.
  • The Cofinality of the Strong Measure Zero Ideal.Teruyuki Yorioka - 2002 - Journal of Symbolic Logic 67 (4):1373-1384.
    We give a characterization of the cofinality of the strong measure zero ideal under the continuum hypothesis and prove that we can force it to a value less than the power of the continuum.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  • Mad Families, Splitting Families and Large Continuum.Jörg Brendle & Vera Fischer - 2011 - Journal of Symbolic Logic 76 (1):198 - 208.
    Let κ < λ be regular uncountable cardinals. Using a finite support iteration (in fact a matrix iteration) of ccc posets we obtain the consistency of b = a = κ < s = λ. If μ is a measurable cardinal and μ < κ < λ, then using similar techniques we obtain the consistency of b = κ < a = s = λ.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   12 citations  
  • The Cardinal Coefficients of the Ideal $${{\Mathcal {I}}_{F}}$$.Noboru Osuga & Shizuo Kamo - 2008 - Archive for Mathematical Logic 47 (7-8):653-671.
    In 2002, Yorioka introduced the σ-ideal ${{\mathcal {I}}_f}$ for strictly increasing functions f from ω into ω to analyze the cofinality of the strong measure zero ideal. For each f, we study the cardinal coefficients (the additivity, covering number, uniformity and cofinality) of ${{\mathcal {I}}_f}$.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  • Iterations of Boolean Algebras with Measure.Anastasis Kamburelis - 1989 - Archive for Mathematical Logic 29 (1):21-28.
    We consider a classM of Boolean algebras with strictly positive, finitely additive measures. It is shown thatM is closed under iterations with finite support and that the forcing via such an algebra does not destroy the Lebesgue measure structure from the ground model. Also, we deduce a simple characterization of Martin's Axiom reduced to the classM.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  • On the Consistency Strength of the Milner–Sauer Conjecture.Assaf Rinot - 2006 - Annals of Pure and Applied Logic 140 (1):110-119.
    In their paper from 1981, Milner and Sauer conjectured that for any poset P,≤, if , then P must contain an antichain of cardinality κ. The conjecture is consistent and known to follow from GCH-type assumptions. We prove that the conjecture has large cardinals consistency strength in the sense that its negation implies, for example, the existence of a measurable cardinal in an inner model. We also prove that the conjecture follows from Martin’s Maximum and holds for all singular λ (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  • Coherent Systems of Finite Support Iterations.Vera Fischer, Sy D. Friedman, Diego A. Mejía & Diana C. Montoya - 2018 - Journal of Symbolic Logic 83 (1):208-236.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  • 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 (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  • Set Theory: On the Structure of the Real Line.T. Bartoszyński & H. Judah - 1999 - Studia Logica 62 (3):444-445.
  • Adding Dominating Reals With $Omega^Omega$ Bounding Posets.Janusz Pawlikowski - 1992 - Journal of Symbolic Logic 57 (2):540-547.
  • The Covering Number and the Uniformity of the Ideal ℐf.Noboru Osuga - 2006 - Mathematical Logic Quarterly 52 (4):351-358.