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Chromatic number Strong coloring Hindman's Theorem Non-saturation xbox positive partition relation polarized partition relation Filter reflection Cardinal function Cardinal Invariants very good scale Aronszajn tree Coherent tree Dowker space incompactness PFA Fodor-type reflection nonmeager set weak diamond Amenable C-sequence Diamond Generalized Clubs Selective Ultrafilter Singular cardinals combinatorics Almost Souslin stick Strongly Luzin set Sakurai's Bell inequality Mandelbrot set diamond star club_AD specializable Souslin tree Absoluteness Closed coloring stationary reflection tensor product graph Knaster Subnormal ideal Greatly Mahlo Ascent Path Reflecting stationary set Singular cofinality Club Guessing b-scale OCA Hedetniemi's conjecture Erdos-Hajnal graphs HOD Rado's conjecture Reduced Power O-space AIM forcing Erdos Cardinal Distributive tree Partition Relations Ineffable cardinal PFA(S)[S] Local Club Condensation. square Square-Brackets Partition Relations Uniformly coherent higher Baire space Almost countably chromatic unbounded function transformations Vanishing levels Souslin Tree Whitehead Problem approachability ideal Luzin set Commutative cancellative semigroups stationary hitting weak square Almost-disjoint family ZFC construction regressive Souslin tree Rainbow sets Fat stationary set Knaster and friends Poset Forcing Axioms Hereditarily Lindelöf space Subtle cardinal Ramsey theory over partitions Singular Density coloring number Analytic sets projective Boolean algebra super-Souslin tree Microscopic Approach P-Ideal Dichotomy Rock n' Roll Uniformly homogeneous Constructible Universe Forcing Precaliber Sierpinski's onto mapping principle Fast club Iterated forcing Weakly compact cardinal Jonsson cardinal square principles ccc Uniformization Open Access free Boolean algebra L-space full tree Subtle tree property Parameterized proxy principle Shelah's Strong Hypothesis Large Cardinals Small forcing Axiom R Ulam matrix Postprocessing function Lipschitz reduction Prevalent singular cardinals Minimal Walks Generalized descriptive set theory S-Space Foundations 54G20 middle diamond sap Slim tree Martin's Axiom Chang's conjecture free Souslin tree Antichain C-sequence Nonspecial tree Successor of Regular Cardinal Ostaszewski square GMA Subadditive strongly bounded groups Universal Sequences countably metacompact Successor of Singular Cardinal Diamond-sharp Diamond for trees Kurepa Hypothesis Dushnik-Miller weak Kurepa tree Was Ulam right Prikry-type forcing Cohen real SNR Well-behaved magma Sigma-Prikry indecomposable ultrafilter reflection principles
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Universal binary sequences
Notation. Write $\mathcal Q(A):=\{ a\subseteq A\mid a\text{ is finite}, a\neq\emptyset\}$. Suppose for the moment that we are given a fixed sequence $\langle f_\alpha:\omega\rightarrow2\mid \alpha\in a\rangle$, indexed by some set $a$ of ordinals. Then, for every function $h:a\rightarrow\omega$ and $i<\omega$, we … Continue reading