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