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