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