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Partition Relations Singular cofinality Forcing Axioms Diamond sap Strongly compact cardinal Reduced Power Minimal Walks positive partition relation Precaliber Greatly Mahlo Subnormal ideal weak diamond Ostaszewski square Cardinal Invariants PFA Poset Luzin set Open Access Foundations Rock n' Roll AIM forcing Club Guessing Analytic sets specializable Souslin tree Well-behaved magma Monotonically far Chang's conjecture square principles reflection principles projective Boolean algebra Uniformly homogeneous Fodor-type reflection Mandelbrot set b-scale O-space weak Kurepa tree Microscopic Approach Non-saturation Knaster and friends Knaster Rado's conjecture Ineffable cardinal Uniformly coherent Reflecting stationary set Martin's Axiom very good scale Diamond for trees unbounded function Successor of Singular Cardinal xbox ccc Almost-disjoint family Respecting tree Distributive tree Subtle cardinal Successor of Regular Cardinal Shelah's Strong Hypothesis Singular cardinals combinatorics Diamond-sharp higher Baire space Nonspecial tree free Souslin tree Prevalent singular cardinals Was Ulam right? Chromatic number Commutative cancellative semigroups Interval topology on trees Strongly Luzin set Closed coloring S-Space club_AD Large Cardinals Singular Density Cohen real PFA(S)[S] stationary reflection Filter reflection countably metacompact Whitehead Problem Generalized Clubs Sakurai's Bell inequality indecomposable filter tensor product graph Almost Souslin Dowker space SNR Cardinal function Forcing with side conditions Commutative projection system Lipschitz reduction Parameterized proxy principle Axiom R Sigma-Prikry Hedetniemi's conjecture coloring number full tree Local Club Condensation. Selective Ultrafilter Fat stationary set regressive Souslin tree Entangled linear order Erdos Cardinal Dushnik-Miller Countryman line L-space Aronszajn tree GMA Vanishing levels square Small forcing stationary hitting Hindman's Theorem Partition relations for trees Universal Sequences Forcing perfectly normal approachability ideal Absoluteness Square-Brackets Partition Relations Prikry-type forcing Postprocessing function Subadditive Ascent Path transformations Ascending path Souslin Tree Fast club Erdos-Hajnal graphs incompactness Jonsson cardinal Amenable C-sequence Rainbow sets Generalized descriptive set theory Constructible Universe Slim tree Almost countably chromatic free Boolean algebra Weakly compact cardinal weak square super-Souslin tree nonmeager set Kurepa Hypothesis Ulam matrix P-Ideal Dichotomy strongly bounded groups stick Subtle tree property Sierpinski's onto mapping principle Intersection model HOD Ramsey theory over partitions Strong coloring C-sequence OCA Antichain Hereditarily Lindelöf space diamond star Uniformization middle diamond polarized partition relation Iterated forcing ZFC construction Coherent tree 54G20
Tag Archives: Closed coloring
Knaster and friends II: The C-sequence number
Joint work with Chris Lambie-Hanson. Abstract. Motivated by a characterization of weakly compact cardinals due to Todorcevic, we introduce a new cardinal characteristic, the C-sequence number, which can be seen as a measure of the compactness of a regular uncountable … Continue reading
The 15th International Workshop on Set Theory in Luminy, September 2019
I gave an invited talk at the 15th International Workshop on Set Theory in Luminy in Marseille, September 2019. Talk Title: Chain conditions, unbounded colorings and the C-sequence spectrum. Abstract: The productivity of the $\kappa$-chain condition, where $\kappa$ is a regular, … Continue reading
Posted in Invited Talks
Tagged Closed coloring, Knaster, Precaliber, stationary reflection, unbounded function
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Knaster and friends I: Closed colorings and precalibers
Joint work with Chris Lambie-Hanson. Abstract. The productivity of the $\kappa$-chain condition, where $\kappa$ is a regular, uncountable cardinal, has been the focus of a great deal of set-theoretic research. In the 1970s, consistent examples of $\kappa$-cc posets whose squares … Continue reading
