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