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