Universal Generalized Computable Numberings and Hyperimmunity
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Generalized computable numberings relative to hyperimmune and high oracles are studied. We give a description of oracles relative to which every finite computable family has a universal computable numbering. Also we present a characterization of the class of oracles relative to which every universal computable numbering of an arbitrary finite family is precomplete, and establish a sufficient condition for universal generalized computable numberings to be precomplete. In addition, we look into the question on limitedness of universal numberings computable relative to high oracles.
Keywordsgeneralized computable numbering universal numbering precomplete numbering hyperimmune set high set
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- 2.S. A. Badaev and S. S. Goncharov, “Theory of numberings: Open problems,” in Computability Theory and Its Applications, Cont. Math., 257, Am. Math. Soc., Providence, RI (2000), pp. 23-38.Google Scholar
- 5.S. A. Badaev and S. S. Goncharov, “Computability and numberings,” in New ComputationalParadigms, S. B. Cooper, B. Lowe, and A. Sorbi (eds.), Springer, New York (2008), pp. 19-34.Google Scholar
- 7.Yu. L. Ershov, Theory of Numerations [in Russian], Nauka, Moscow (1977).Google Scholar
- 8.Yu. L. Ershov, “Theory of numberings,” in Handbook of Computability Theory, Stud. Log. Found. Math., 140, North-Holland, Amsterdam (1999), pp. 473-503.Google Scholar
- 10.S. A. Badaev and A. A. Isakhov, “A-computable numberings,” Mal’tsev Readings, (2015), p. 61.Google Scholar