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