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weak square very good scale Antichain Minimal Walks Singular Density Parameterized proxy principle Successor of Singular Cardinal incompactness L-space SNR reflection principles Knaster and friends Coherent tree Reflecting stationary set Slim tree nonmeager set regressive Souslin tree P-Ideal Dichotomy OCA Generalized Clubs Iterated forcing Diamond for trees Subtle cardinal Ostaszewski square Forcing Axioms countably metacompact Partition Relations Selective Ultrafilter Uniformly homogeneous full tree Singular cardinals combinatorics Sakurai's Bell inequality Lipschitz reduction Prevalent singular cardinals Generalized descriptive set theory Foundations Cohen real weak diamond PFA Uniformization indecomposable ultrafilter Successor of Regular Cardinal Analytic sets Hedetniemi's conjecture positive partition relation Erdos-Hajnal graphs Axiom R Rado's conjecture tensor product graph PFA(S)[S] Vanishing levels Commutative projection system Almost countably chromatic Small forcing Square-Brackets Partition Relations Almost-disjoint family Diamond-sharp Whitehead Problem Commutative cancellative semigroups middle diamond xbox GMA Chang's conjecture Uniformly coherent Was Ulam right Countryman line stationary hitting Almost Souslin specializable Souslin tree Forcing Large Cardinals Poset O-space Fat stationary set Kurepa Hypothesis Microscopic Approach stationary reflection transformations Shelah's Strong Hypothesis ZFC construction Prikry-type forcing stick Distributive tree Strong coloring Jonsson cardinal Strongly compact cardinal Ramsey theory over partitions Non-saturation Well-behaved magma Nonspecial tree unbounded function Erdos Cardinal Ascent Path Postprocessing function Dushnik-Miller 54G20 b-scale Knaster Constructible Universe C-sequence Rock n' Roll Martin's Axiom Fodor-type reflection Singular cofinality Cardinal function sap Fast club Club Guessing square Amenable C-sequence Intersection model Ulam matrix strongly bounded groups Weakly compact cardinal ccc S-Space Rainbow sets Aronszajn tree free Boolean algebra Absoluteness HOD square principles Universal Sequences Sigma-Prikry Diamond Cardinal Invariants Local Club Condensation. super-Souslin tree Precaliber Greatly Mahlo Ineffable cardinal polarized partition relation Closed coloring Dowker space Souslin Tree weak Kurepa tree Strongly Luzin set higher Baire space Sierpinski's onto mapping principle Reduced Power Chromatic number Subadditive approachability ideal Luzin set Hereditarily Lindelöf space Filter reflection Respecting tree Hindman's Theorem club_AD Subtle tree property free Souslin tree Mandelbrot set coloring number Open Access AIM forcing Subnormal ideal diamond star projective Boolean algebra
Tag Archives: sap
Knaster and friends III: Subadditive colorings
Joint work with Chris Lambie-Hanson. Abstract. We continue our study of strongly unbounded colorings, this time focusing on subadditive maps. In Part I of this series, we showed that, for many pairs of infinite cardinals $\theta < \kappa$, the existence … Continue reading
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
The failure of diamond on a reflecting stationary set
Joint work with Moti Gitik. Abstract: It is shown that the failure of $\diamondsuit_S$, for a subset $S\subseteq\aleph_{\omega+1}$ that reflects stationarily often, is consistent with GCH and $\text{AP}_{\aleph_\omega}$, relatively to the existence of a supercompact cardinal. This should be comapred with … 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
