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