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Positive Numberings of Families of Sets in the Ershov Hierarchy
Authors:Zh T Talasbaeva
Institution:(1) Kazakhstan State University, Masanchi 39/47, Almaty, 480012, Kazakhstan
Abstract:It is proved that there exist infinitely many positive undecidable Sgr n -1 -computable numberings of every infinite family 
$$S \subseteq \Sigma _n^{ - 1}$$
that admits at least one Sgr n -1 -computable numbering and contains either the empty set, for even n, or N for odd n.
Keywords:Ershov hierarchy  positive undecidable Sgr n -1 -computable numbering" target="_blank">gif" alt="Sgr" align="BASELINE" BORDER="0"> n -1 -computable numbering
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