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Erdos Cardinal Precaliber OCA Forcing Axioms free Boolean algebra Rainbow sets Fodor-type reflection Cardinal function GMA Dowker space Non-saturation approachability ideal unbounded function weak Kurepa tree Almost Souslin Antichain sap Successor of Singular Cardinal stationary hitting C-sequence stationary reflection Uniformization coloring number square Knaster and friends club_AD polarized partition relation Large Cardinals Subtle tree property Greatly Mahlo AIM forcing Diamond for trees Whitehead Problem Luzin set Diamond Weakly compact cardinal Fast club Nonspecial tree Singular cardinals combinatorics incompactness Intersection model Monotonically far Successor of Regular Cardinal projective Boolean algebra Distributive tree Lipschitz reduction Shelah's Strong Hypothesis Prevalent singular cardinals PFA(S)[S] Partition Relations Generalized Clubs Chromatic number Constructible Universe Fat stationary set Ramsey theory over partitions Coherent tree HOD Reflecting stationary set Club Guessing Countryman line Erdos-Hajnal graphs Iterated forcing Rado's conjecture L-space Forcing with side conditions Square-Brackets Partition Relations SNR PFA indecomposable filter Strongly Luzin set Well-behaved magma Filter reflection Souslin Tree strongly bounded groups Closed coloring Knaster Uniformly homogeneous super-Souslin tree Commutative cancellative semigroups countably metacompact Interval topology on trees Foundations Cardinal Invariants Forcing Kurepa Hypothesis Microscopic Approach nonmeager set full tree Ascending path Ineffable cardinal Minimal Walks Axiom R Analytic sets tensor product graph Dushnik-Miller higher Baire space Hedetniemi's conjecture Vanishing levels Uniformly coherent stick Parameterized proxy principle regressive Souslin tree Subnormal ideal ZFC construction S-Space square principles Universal Sequences transformations Selective Ultrafilter Absoluteness Open Access Singular Density perfectly normal Amenable C-sequence specializable Souslin tree Jonsson cardinal Rock n' Roll Generalized descriptive set theory weak square ccc O-space Strongly compact cardinal Sierpinski's onto mapping principle Prikry-type forcing reflection principles Sakurai's Bell inequality Almost-disjoint family Hereditarily Lindelöf space Diamond-sharp Small forcing weak diamond Slim tree Subadditive Entangled linear order Sigma-Prikry Mandelbrot set very good scale b-scale Respecting tree diamond star Singular cofinality Hindman's Theorem Subtle cardinal Local Club Condensation. Almost countably chromatic Ulam matrix 54G20 Commutative projection system xbox P-Ideal Dichotomy Martin's Axiom Partition relations for trees positive partition relation Chang's conjecture Aronszajn tree Ostaszewski square Poset Reduced Power Ascent Path Postprocessing function middle diamond Strong coloring free Souslin tree Cohen real Was Ulam right?
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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