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super-Souslin tree stationary reflection Sigma-Prikry full tree Filter reflection nonmeager set Was Ulam right club_AD Minimal Walks Non-saturation Antichain Whitehead Problem approachability ideal positive partition relation Subadditive Prevalent singular cardinals tensor product graph Fodor-type reflection Precaliber very good scale Partition Relations indecomposable ultrafilter weak square Rock n' Roll Knaster stick Singular Density Universal Sequences Successor of Singular Cardinal Subtle tree property projective Boolean algebra C-sequence Mandelbrot set Rado's conjecture Iterated forcing Cardinal function Ineffable cardinal Parameterized proxy principle Rainbow sets Vanishing levels OCA Luzin set SNR Ramsey theory over partitions Almost countably chromatic xbox Uniformization square Generalized Clubs Axiom R Almost-disjoint family Souslin Tree Kurepa Hypothesis AIM forcing unbounded function Aronszajn tree Successor of Regular Cardinal O-space PFA(S)[S] Hedetniemi's conjecture L-space incompactness transformations Amenable C-sequence Absoluteness Sakurai's Bell inequality Sierpinski's onto mapping principle Prikry-type forcing Club Guessing Strong coloring Distributive tree regressive Souslin tree Closed coloring S-Space Subnormal ideal Foundations ccc b-scale Generalized descriptive set theory strongly bounded groups countably metacompact Microscopic Approach diamond star Local Club Condensation. Shelah's Strong Hypothesis ZFC construction Open Access Erdos Cardinal Knaster and friends Dowker space free Souslin tree Subtle cardinal Dushnik-Miller Ulam matrix Singular cofinality Strongly Luzin set weak diamond GMA Slim tree Singular cardinals combinatorics Cardinal Invariants free Boolean algebra Constructible Universe P-Ideal Dichotomy stationary hitting Fast club reflection principles Reduced Power coloring number Martin's Axiom sap Weakly compact cardinal Square-Brackets Partition Relations Uniformly coherent Ostaszewski square 54G20 specializable Souslin tree Commutative cancellative semigroups Jonsson cardinal Diamond-sharp middle diamond Reflecting stationary set Cohen real Hindman's Theorem Lipschitz reduction Coherent tree HOD Nonspecial tree Almost Souslin higher Baire space Analytic sets Large Cardinals Hereditarily Lindelöf space PFA Well-behaved magma Ascent Path Erdos-Hajnal graphs Fat stationary set square principles Small forcing Selective Ultrafilter weak Kurepa tree Chromatic number Postprocessing function Greatly Mahlo Uniformly homogeneous Diamond for trees polarized partition relation Poset Forcing Diamond Forcing Axioms Chang's conjecture
Tag Archives: stationary hitting
Jensen’s diamond principle and its relatives
This is chapter 6 in the book Set Theory and Its Applications (ISBN: 0821848127). Abstract: We survey some recent results on the validity of Jensen’s diamond principle at successor cardinals. We also discuss weakening of this principle such as club … Continue reading
A relative of the approachability ideal, diamond and non-saturation
Abstract: Let $\lambda$ denote a singular cardinal. Zeman, improving a previous result of Shelah, proved that $\square^*_\lambda$ together with $2^\lambda=\lambda^+$ implies $\diamondsuit_S$ for every $S\subseteq\lambda^+$ that reflects stationarily often. In this paper, for a subset $S\subset\lambda^+$, a normal subideal of … Continue reading