Abstract
The strongest type of coloring of pairs of countable ordinals, gotten by Todorčević from a strongly Luzin set, is shown to be equivalent to the existence of a nonmeager set of reals of size ℵ 1 \aleph _1 . In the other direction, it is shown that the existence of both a strongly Luzin set and a coherent Souslin tree is compatible with the existence of a countable partition of pairs of countable ordinals such that no coloring is strong over it. This clarifies the interaction between a gallery of coloring assertions going back to Luzin and Sierpiński a hundred years ago.
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