Hyperimmunity and A-computable universal numberings

Alibek Issakhov

2016

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DOI 10.1063/1.4959720
Data confidence 70 medium
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Abstract

Whether there exists a computable universal numbering for a computable family is the key question in theory of numberings. In a very general setting, this problem was explored in [Yu. L. Ershov, Theory of Numberings, Handbook of Computability Theory, North-Holland; Amsterdam: Stud. Log. Found. Math., Vol. 140, pp. 473–503, 1999]. For sets A that are Turing jumps of the empty set, the problem was treated in [S. A. Badaev, S. S. Goncharov, and A. Sorbi, Computability and Models, 11–44 (2003)] and other papers. In this work, we investigate families of total functions computable relative to hyperimmune and hyperimmune-free oracles.