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