We show that for every ordinal notation \xi of a nonzero computable ordinal, there exists a Sigma_\xi—computable family which up to equivalence has exactly one Friedberg numbering, which does not induce the least element in the corresponding Rogers semilattice.

Serikzhan A., B., Mustafa, M., & Sorbi, A. (2015). Friedberg numberings in the Ershov hierarchy. ARCHIVE FOR MATHEMATICAL LOGIC, 54(1-2), 59-73 [10.1007/s00153-014-0402-y].

### Friedberg numberings in the Ershov hierarchy

#### Abstract

We show that for every ordinal notation \xi of a nonzero computable ordinal, there exists a Sigma_\xi—computable family which up to equivalence has exactly one Friedberg numbering, which does not induce the least element in the corresponding Rogers semilattice.
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