A remark on pseudojump operators
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- by A. H. Lachlan and X. Yi PDF
- Proc. Amer. Math. Soc. 106 (1989), 489-491 Request permission
Abstract:
Let ${\left \{ {{W_n}} \right \}_{n \in \omega }}$ be an enumeration of the recursively enumerable sets. In answer to a question of Jockusch and Shore we show that there exist $i$ and $j$ such that for all $e$ either ${W_e}$ is recursive or at least one of $({W_e} \oplus W_i^{{W_e}})$ and $({W_e} \oplus W_j^{{W_e}})$ is not recursively enumerable.References
- Carl G. Jockusch Jr. and Richard A. Shore, Pseudojump operators. I. The r.e. case, Trans. Amer. Math. Soc. 275 (1983), no. 2, 599–609. MR 682720, DOI 10.1090/S0002-9947-1983-0682720-1
- Robert I. Soare, Recursively enumerable sets and degrees, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1987. A study of computable functions and computably generated sets. MR 882921, DOI 10.1007/978-3-662-02460-7
- Robert I. Soare and Michael Stob, Relative recursive enumerability, Proceedings of the Herbrand symposium (Marseilles, 1981) Stud. Logic Found. Math., vol. 107, North-Holland, Amsterdam, 1982, pp. 299–324. MR 757037, DOI 10.1016/S0049-237X(08)71892-5
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 106 (1989), 489-491
- MSC: Primary 03D25
- DOI: https://doi.org/10.1090/S0002-9939-1989-0937847-4
- MathSciNet review: 937847