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