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