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Coherent tree Shelah's Strong Hypothesis AIM forcing Jonsson cardinal Generalized Clubs Almost countably chromatic sap Fodor-type reflection Small forcing Vanishing levels Minimal Walks Luzin set Almost Souslin reflection principles Universal Sequences Mandelbrot set full tree ZFC construction Large Cardinals Ascent Path Well-behaved magma Nonspecial tree indecomposable ultrafilter Reflecting stationary set Cardinal Invariants Almost-disjoint family Rado's conjecture ccc super-Souslin tree Subtle cardinal tensor product graph Non-saturation Successor of Regular Cardinal 54G20 Chang's conjecture Prikry-type forcing Singular cofinality regressive Souslin tree middle diamond OCA Hereditarily Lindelöf space countably metacompact Generalized descriptive set theory specializable Souslin tree weak square Ostaszewski square Weakly compact cardinal Club Guessing Parameterized proxy principle Commutative cancellative semigroups Iterated forcing Fast club Sigma-Prikry diamond star unbounded function coloring number Uniformization Lipschitz reduction nonmeager set Distributive tree approachability ideal Closed coloring Dushnik-Miller Axiom R Foundations Antichain Open Access Cohen real Strongly Luzin set higher Baire space Greatly Mahlo projective Boolean algebra incompactness Uniformly homogeneous Aronszajn tree Square-Brackets Partition Relations Knaster and friends P-Ideal Dichotomy positive partition relation stationary reflection square Slim tree Martin's Axiom Precaliber Amenable C-sequence Forcing Axioms O-space Filter reflection strongly bounded groups PFA(S)[S] transformations Rainbow sets L-space PFA Cardinal function free Souslin tree C-sequence Hindman's Theorem Kurepa Hypothesis Subtle tree property Knaster Diamond for trees Microscopic Approach Absoluteness SNR Diamond Erdos-Hajnal graphs weak diamond Constructible Universe Erdos Cardinal stick HOD Analytic sets Rock n' Roll Souslin Tree Fat stationary set Reduced Power xbox Chromatic number free Boolean algebra very good scale Ulam matrix GMA Subadditive Postprocessing function Singular Density Selective Ultrafilter Subnormal ideal Local Club Condensation. Poset stationary hitting Prevalent singular cardinals Dowker space Hedetniemi's conjecture Ineffable cardinal Successor of Singular Cardinal Whitehead Problem Forcing Sierpinski's onto mapping principle Strong coloring b-scale Sakurai's Bell inequality polarized partition relation square principles club_AD Singular cardinals combinatorics Partition Relations Uniformly coherent Diamond-sharp Was Ulam right Ramsey theory over partitions S-Space
Tag Archives: Generalized Clubs
The failure of diamond on a reflecting stationary set
Joint work with Moti Gitik. Abstract: It is shown that the failure of $\diamondsuit_S$, for a subset $S\subseteq\aleph_{\omega+1}$ that reflects stationarily often, is consistent with GCH and $\text{AP}_{\aleph_\omega}$, relatively to the existence of a supercompact cardinal. This should be comapred with … 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