Positive undecidable numberings in the Ershov hierarchy (Q695803)

In the paper under review the authors give a sufficient condition under which an infinite computable family of \(\Sigma^{-1}_a\) sets has computable positive but undecidable numberings. Here \(a\) is a notation for a computable ordinal \(>0\). In particular, it is shown that if \(a\) is a notation for an infinite computable ordinal and \({\mathcal A}\) is an infinite family of \(\Sigma^{-1}_a\) sets containing an \(n\)-c.e. set, then \({\mathcal A}\) has infinitely many computable positive undecidable numberings, which are pairwise incomparable with respect to Rogers reducibility.