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