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xbox Universal Sequences Cardinal function Uniformly coherent Almost countably chromatic Subnormal ideal Luzin set Weakly compact cardinal Monotonically far Chang's conjecture Axiom R Small forcing Chromatic number weak diamond Ramsey theory over partitions Shelah's Strong Hypothesis Hereditarily Lindelöf space countably metacompact Filter reflection perfectly normal stationary hitting C-sequence Singular cofinality Square-Brackets Partition Relations Analytic sets Strong coloring Hedetniemi's conjecture Forcing Partition relations for trees Countryman line HOD Iterated forcing sap Erdos-Hajnal graphs club_AD Prevalent singular cardinals Absoluteness weak Kurepa tree reflection principles Cardinal Invariants Was Ulam right? square Rado's conjecture Dowker space Constructible Universe Jonsson cardinal Martin's Axiom Diamond OCA Club Guessing L-space Interval topology on trees Fast club Partition Relations regressive Souslin tree Slim tree b-scale specializable Souslin tree S-Space Respecting tree Nonspecial tree Ulam matrix Knaster Erdos Cardinal Rainbow sets Sigma-Prikry Local Club Condensation. free Boolean algebra Generalized Clubs diamond star Entangled linear order 54G20 PFA Subtle cardinal square principles PFA(S)[S] strongly bounded groups Aronszajn tree Knaster and friends Greatly Mahlo Large Cardinals GMA Reduced Power projective Boolean algebra SNR Forcing Axioms Successor of Regular Cardinal Uniformly homogeneous unbounded function transformations nonmeager set Sierpinski's onto mapping principle Mandelbrot set Microscopic Approach Dushnik-Miller Lipschitz reduction ZFC construction Poset Fat stationary set Coherent tree stick Vanishing levels stationary reflection AIM forcing middle diamond Minimal Walks super-Souslin tree Rock n' Roll Distributive tree Souslin Tree positive partition relation Closed coloring Antichain Open Access Selective Ultrafilter Hindman's Theorem Almost Souslin Well-behaved magma incompactness higher Baire space Successor of Singular Cardinal Non-saturation Kurepa Hypothesis indecomposable filter Precaliber Diamond-sharp Intersection model Generalized descriptive set theory Commutative cancellative semigroups free Souslin tree very good scale coloring number Singular Density Ascending path Prikry-type forcing Cohen real Almost-disjoint family Ineffable cardinal ccc Strongly compact cardinal Sakurai's Bell inequality Reflecting stationary set full tree Parameterized proxy principle Commutative projection system approachability ideal O-space Fodor-type reflection Subadditive Amenable C-sequence tensor product graph polarized partition relation Postprocessing function weak square Diamond for trees P-Ideal Dichotomy Ascent Path Uniformization Singular cardinals combinatorics Forcing with side conditions Foundations Ostaszewski square Strongly Luzin set Whitehead Problem Subtle tree property
Tag Archives: Knaster
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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11th Young Set Theory Workshop, June 2018
I gave a 4-lecture tutorial at the 11th Young Set Theory Workshop, Lausanne, June 2018. Title: In praise of C-sequences. Abstract. Ulam and Solovay showed that any stationary set may be split into two. Is it also the case that … Continue reading
Posted in Invited Talks
Tagged Aronszajn tree, C-sequence, incompactness, Knaster, Minimal Walks, Postprocessing function, square
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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
c.c.c. vs. the Knaster property
After my previous post on Mekler’s characterization of c.c.c. notions of forcing, Sam, Mike and myself discussed the value of it . We noticed that a prevalent verification of the c.c.c. goes like this: given an uncountable set of conditions, … Continue reading
