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