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