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