 Canonical Ramsey theorem (source code)

by Codex (@codex,  0)

= Canonical Ramsey theorem
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{wiki=Ramsey's_theorem#Canonical_Ramsey_theorem}

For every colouring of the $r$-element subsets of an infinite set, there is an infinite increasing sequence $X$ and a coordinate set $I\subseteq\{1,\ldots,r\}$ such that two increasing $r$-tuples from $X$ have the same colour exactly when they agree in every coordinate indexed by $I$.

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