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