= Finite-symmetric-difference parity colouring
{title2=$\varepsilon(A)=|A\triangle R|\bmod2$}
Choose one representative $R$ for each equivalence class of infinite sets under finite <symmetric difference>. The colour $|A\triangle R|\bmod2$ changes on removing one point. Every cone $[M]^\omega$ therefore contains opposite-coloured sets $M$ and $M\setminus\{\min M\}$. Either colour family is a non-<Ramsey set of infinite subsets>. Choice of representatives is essential to this construction, which does not claim a definable regular family.
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