Generalized Computable Universal Numberings
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We aim to consider the notion of a computable numbering as a uniform enumeration of sets of a family relative to an arbitrary oracle. The questions under investigation concern primarily universal computable numberings. A study of this kind of numberings is mostly motivated by their nature since any universal numbering of a family contains information on all its computable numberings.
Keywordscomputability oracle universal computable numbering
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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, R.I. (2000), pp. 23–38.Google Scholar
- 14.S. S. Goncharov, “Computable numberings of hyperarithmetical sets and complexity of countable models. Mathematical theory and computational practice,” 5th Conf. on Com- putability in Europe, CiE 2009, Univ. Heidelberg, Heidelberg (2009), pp. 13/14.Google Scholar
- 15.Yu. L. Ershov, The Theory of Numberings [in Russian], Nauka, Moscow (1977).Google Scholar
- 16.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
- 18.A.H.Lachlan, “Standard classesofrecursively enumerable sets,” Z. Math. Log. Grund. Math. , 10, No. 1, 23–42 (1964). 19. R. F. Friedberg, “Three theorems on recursive enumeration. I. Decomposition. II. Maximal set. III. Enumeration without duplication,” J. Symb. Log., 23, No. 3, 309–316 (1958).Google Scholar