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