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unbounded function Knaster Square-Brackets Partition Relations Countryman line Partition Relations Diamond-sharp club_AD Postprocessing function Ramsey theory over partitions Jonsson cardinal Poset Axiom R Diamond for trees stick Iterated forcing O-space Singular cardinals combinatorics Sigma-Prikry ZFC construction specializable Souslin tree Ineffable cardinal ccc Souslin Tree Diamond strongly bounded groups Fodor-type reflection Subadditive Precaliber Reduced Power coloring number sap Hedetniemi's conjecture Minimal Walks regressive Souslin tree Erdos Cardinal Absoluteness Non-saturation incompactness Strongly compact cardinal Uniformly homogeneous diamond star Monotonically far Ascending path Slim tree Cardinal Invariants perfectly normal Ulam matrix PFA approachability ideal Generalized Clubs Knaster and friends Amenable C-sequence weak square very good scale Hereditarily Lindelöf space Antichain Subnormal ideal Weakly compact cardinal Interval topology on trees AIM forcing Closed coloring Respecting tree projective Boolean algebra Whitehead Problem SNR GMA PFA(S)[S] Subtle tree property positive partition relation Large Cardinals Sakurai's Bell inequality Ascent Path Commutative projection system nonmeager set Local Club Condensation. Well-behaved magma b-scale Constructible Universe Partition relations for trees Singular cofinality Forcing Axioms Lipschitz reduction Filter reflection Greatly Mahlo Nonspecial tree Chang's conjecture weak Kurepa tree weak diamond reflection principles middle diamond Fast club indecomposable filter Selective Ultrafilter countably metacompact Dowker space Uniformization Chromatic number Strongly Luzin set Almost Souslin Singular Density stationary hitting Successor of Singular Cardinal OCA Ostaszewski square HOD Shelah's Strong Hypothesis Parameterized proxy principle Hindman's Theorem Generalized descriptive set theory Intersection model Mandelbrot set Small forcing Universal Sequences free Boolean algebra 54G20 Uniformly coherent Entangled linear order Martin's Axiom Prikry-type forcing Club Guessing Cardinal function Sierpinski's onto mapping principle Rock n' Roll super-Souslin tree Almost-disjoint family transformations L-space full tree Was Ulam right? Successor of Regular Cardinal S-Space Almost countably chromatic C-sequence Rainbow sets Microscopic Approach Commutative cancellative semigroups Forcing stationary reflection Vanishing levels Aronszajn tree Coherent tree Cohen real Reflecting stationary set Foundations Dushnik-Miller Forcing with side conditions Kurepa Hypothesis Strong coloring P-Ideal Dichotomy Distributive tree tensor product graph Rado's conjecture higher Baire space square polarized partition relation xbox square principles Fat stationary set Analytic sets Luzin set Open Access Erdos-Hajnal graphs Subtle cardinal Prevalent singular cardinals free Souslin tree
Tag Archives: OCA
Open coloring and the cardinal invariant $\mathfrak b$
Nik Weaver asked for a direct proof of the fact that Todorcevic’s axiom implies the failure of CH fails. Here goes. Notation. For a set $X$, we write $[X]^2$ for the set of unordered pairs $\{ \{x,x’\}\mid x,x’\in X, x\neq … Continue reading
