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