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