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