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