We show that for every n 1, there exists a 1n -computable family which up to equivalence has exactly one Friedberg numbering which does not induce the least element of the corresponding Rogers semilattice.
We give a su cient condition for an in nite computable family of 1
a sets, to have computable positive but undecidable numberings, where a
is a notation for a nonzero computable ordinal. This extends a theorem
proved ...
Let a be a Kleene's ordinal notation of a nonzero computable ordinal. We give a su cient condition on a, so that for every 1 a {computable family of two embedded sets, i.e. two sets A;B, with A properly contined in B, ...
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