Σ5-completeness of index sets arising from the recursively enumerable Turing degrees Original Research Article

We employ techniques related to Lempp and Lermanʹs “iterated trees of strategies” to directly measure a Σ5-predicate and use this in showing the index set of the cuppable r.e. sets to be Σ5-complete. We also show how certain technical devices arise naturally out of the iterated-trees context, in particular, links arise as manifestations of a generalized notion of “stage”.