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Almost-disjoint family Singular Density Strongly compact cardinal Martin's Axiom Almost Souslin Distributive tree Kurepa Hypothesis Uniformly coherent Successor of Singular Cardinal Cohen real nonmeager set Constructible Universe very good scale countably metacompact Club Guessing indecomposable ultrafilter Rainbow sets regressive Souslin tree coloring number higher Baire space unbounded function approachability ideal transformations ccc Diamond SNR Non-saturation OCA Local Club Condensation. Cardinal Invariants Amenable C-sequence specializable Souslin tree free Souslin tree Prevalent singular cardinals Generalized Clubs Ostaszewski square Erdos-Hajnal graphs Sakurai's Bell inequality Mandelbrot set 54G20 Jonsson cardinal Analytic sets Forcing Reflecting stationary set Parameterized proxy principle xbox Almost countably chromatic Fodor-type reflection reflection principles Forcing Axioms weak Kurepa tree stationary reflection Square-Brackets Partition Relations strongly bounded groups projective Boolean algebra Open Access Subadditive diamond star Subtle cardinal Uniformly homogeneous stick Foundations PFA Small forcing Whitehead Problem Successor of Regular Cardinal Microscopic Approach Hindman's Theorem Poset Coherent tree Greatly Mahlo P-Ideal Dichotomy Vanishing levels Prikry-type forcing full tree ZFC construction L-space Subnormal ideal Closed coloring Lipschitz reduction sap Filter reflection Respecting tree Weakly compact cardinal Partition Relations Uniformization incompactness Strong coloring square principles Luzin set O-space Iterated forcing Sierpinski's onto mapping principle Ulam matrix Sigma-Prikry Antichain Countryman line Singular cardinals combinatorics super-Souslin tree Diamond-sharp Dowker space Rock n' Roll Souslin Tree Subtle tree property Large Cardinals Minimal Walks Commutative projection system Reduced Power Cardinal function stationary hitting Rado's conjecture Precaliber positive partition relation free Boolean algebra Shelah's Strong Hypothesis Knaster b-scale Axiom R C-sequence PFA(S)[S] Slim tree Chang's conjecture Singular cofinality club_AD weak square Nonspecial tree Intersection model polarized partition relation Commutative cancellative semigroups tensor product graph Universal Sequences Selective Ultrafilter Fast club Hereditarily Lindelöf space Absoluteness Aronszajn tree AIM forcing Generalized descriptive set theory HOD Diamond for trees weak diamond S-Space GMA Ineffable cardinal Fat stationary set square Chromatic number Well-behaved magma Dushnik-Miller Strongly Luzin set Knaster and friends Hedetniemi's conjecture Postprocessing function middle diamond Erdos Cardinal Ramsey theory over partitions Was Ulam right Ascent Path
Tag Archives: Club Guessing
Jensen’s diamond principle and its relatives
This is chapter 6 in the book Set Theory and Its Applications (ISBN: 0821848127). Abstract: We survey some recent results on the validity of Jensen’s diamond principle at successor cardinals. We also discuss weakening of this principle such as club … Continue reading
On guessing generalized clubs at the successors of regulars
Abstract: Konig, Larson and Yoshinobu initiated the study of principles for guessing generalized clubs, and introduced a construction of an higher Souslin tree from the strong guessing principle. Complementary to the author’s work on the validity of diamond and non-saturation … Continue reading
Transforming rectangles into squares, with applications to strong colorings
Abstract: It is proved that every singular cardinal $\lambda$ admits a function $\textbf{rts}:[\lambda^+]^2\rightarrow[\lambda^+]^2$ that transforms rectangles into squares. That is, whenever $A,B$ are cofinal subsets of $\lambda^+$, we have $\textbf{rts}[A\circledast B]\supseteq C\circledast C$, for some cofinal subset $C\subseteq\lambda^+$. As a … Continue reading
The Ostaszewski square, and homogeneous Souslin trees
Abstract: Assume GCH and let $\lambda$ denote an uncountable cardinal. We prove that if $\square_\lambda$ holds, then this may be witnessed by a coherent sequence $\left\langle C_\alpha \mid \alpha<\lambda^+\right\rangle$ with the following remarkable guessing property: For every sequence $\langle A_i\mid i<\lambda\rangle$ … Continue reading
Posted in Publications, Souslin Hypothesis, Squares and Diamonds
Tagged 03E05, 03E35, Club Guessing, Fat stationary set, Ostaszewski square, Souslin Tree
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