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