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