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