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