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