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