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