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