When dealing with a tree (substring closed subset of $\omega^{< \omega})$ a useful operation will frequently be to remove any nodes with finite ordinal rank (i.e., all nodes whose extensions on the tree are bounded in length). This is kinda analagous to the Cantor-Bendixson derivitive but does this operation have a name?
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1$\begingroup$ Since this produces a pruned tree I guess it should be called pruning $\endgroup$– Alessandro CodenottiCommented Oct 29 at 19:04
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1$\begingroup$ In $\omega^{< \omega}$ the result won't be fully pruned (tho when I first published the Tex wasn't rendering). We don't have compactness. But maybe $n$- pruning isn't bad. $\endgroup$– Peter GerdesCommented Oct 29 at 19:24
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