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