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