= Ellentuck Borel sets are completely Ramsey
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Every <Borel set> for the <Ellentuck topology> is <completely Ramsey>. First, an acceptance-and-rejection fusion makes every open set homogeneous after thinning the infinite reservoir while keeping its finite stem. Every nowhere-dense set is consequently <completely Ramsey-null>, and a fusion handling all subsets of each finite selected prefix shows that countable unions of such null sets remain null. Finally, sets differing from an open set by a <meagre set> form a <sigma-algebra> containing the open sets. Thus every Borel set has the required stem-preserving homogeneous refinement.
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