Archives
Keywords
Almost-disjoint family Dowker space Dushnik-Miller Ulam matrix ZFC construction incompactness Constructible Universe Filter reflection Generalized Clubs 54G20 Club Guessing weak square indecomposable filter Greatly Mahlo Diamond-sharp OCA HOD Ramsey theory over partitions Subtle tree property Uniformization Whitehead Problem Countryman line Strongly Luzin set middle diamond Uniformly homogeneous full tree Chang's conjecture Erdos Cardinal Knaster and friends Partition Relations Commutative cancellative semigroups Forcing Axioms specializable Souslin tree Universal Sequences Diamond for trees Cardinal function Small forcing Large Cardinals Poset Subtle cardinal Amenable C-sequence approachability ideal Local Club Condensation. PFA Knaster positive partition relation strongly bounded groups transformations Entangled linear order Interval topology on trees Nonspecial tree diamond star Strongly compact cardinal Distributive tree square Non-saturation PFA(S)[S] Sakurai's Bell inequality Successor of Singular Cardinal Sigma-Prikry polarized partition relation C-sequence Diamond Was Ulam right? Rock n' Roll Souslin Tree Kurepa Hypothesis Singular cofinality Foundations super-Souslin tree Aronszajn tree Fat stationary set Weakly compact cardinal Rado's conjecture weak diamond ccc Ascending path Chromatic number AIM forcing Generalized descriptive set theory Analytic sets square principles Subadditive Selective Ultrafilter Vanishing levels L-space Fodor-type reflection SNR Slim tree Square-Brackets Partition Relations Iterated forcing Axiom R higher Baire space Prikry-type forcing Strong coloring Absoluteness Antichain Almost Souslin Erdos-Hajnal graphs b-scale Ascent Path Uniformly coherent S-Space Intersection model free Boolean algebra GMA xbox Singular cardinals combinatorics Closed coloring Parameterized proxy principle very good scale Lipschitz reduction countably metacompact Prevalent singular cardinals Forcing with side conditions coloring number stationary hitting Successor of Regular Cardinal nonmeager set reflection principles stationary reflection Precaliber Monotonically far Jonsson cardinal perfectly normal Cardinal Invariants Almost countably chromatic weak Kurepa tree Shelah's Strong Hypothesis Mandelbrot set Respecting tree Postprocessing function regressive Souslin tree Hedetniemi's conjecture Hindman's Theorem tensor product graph Minimal Walks Ineffable cardinal Martin's Axiom unbounded function Luzin set O-space projective Boolean algebra Ostaszewski square Fast club Partition relations for trees Reflecting stationary set Open Access sap Hereditarily Lindelöf space Sierpinski's onto mapping principle Microscopic Approach Forcing Rainbow sets stick Cohen real Singular Density Commutative projection system free Souslin tree Reduced Power Coherent tree Well-behaved magma P-Ideal Dichotomy club_AD Subnormal ideal
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
Comments Off on The 15th International Workshop on Set Theory in Luminy, September 2019
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
Leave a comment
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
