Families without Friedberg but with positive numberings in the Ershov hierarchy.
Abstract
We point out that for every ordinal notation a of a nonzero ordinal, there are families of ΣReferences
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[2] S. Badaev and S. Goncharov. The theory of numberings: open problems. / In P. A. Cholak, S. Lempp, M. Lerman, and R. A. Shore, editors, Computability Theory and its Applications, volume 257 of Contemporary Mathematics, pages 23–38. American Mathematical Society, Providence, 2000.
[3] Yu. L. Ershov. A hierarchy of sets, I. // Algebra and Logic, 7:47–73, 1968.
[4] Yu. L. Ershov. A hierarchy of sets, II. // Algebra and Logic, 7:15–47, 1968.
[5] Yu. L. Ershov. A hierarchy of sets, III. // Algebra and Logic, 9:34–51, 1970.
[6] S. Goncharov and A. Sorbi. Generalized computable numerations and non-trivial Rogers semilattices. // Algebra and Logic, 36(6):359–369, 1997.
[7] S. Ospichev. Computable family of
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