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