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It is a well-known elementary classical result in computability theory that there are computable infinite binary trees $T\subset 2^{<\omega}$ having no computable infinite branch. (One can build ...

The (a?) Kleene tree is a computable (a.k.a. decidable) sub-tree of the full binary tree with no computable path. It is well-known. I need a variant. (For those in the know, I need a c-bar which is ...

I'm probably just missing something obvious but suppose that $T \subset 2^{< \omega}$ is a perfect tree with no terminal nodes (what about just $[T]$ non-empty?). If $Y \leq_{T} X$ for all $X \...

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 ...