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