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A remark on pseudojump operators


Authors: A. H. Lachlan and X. Yi
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
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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 [Enhancements On Off] (What's this?)

  • [1] C. G. Jockusch Jr. and R. A. Shore, Pseudo jump operators, I: The R.E. Case, Trans. Amer. Math. Soc. 275 (1983), 599-609. MR 682720 (84c:03081)
  • [2] R. I. Soare, Recursively enumerable sets and degrees, Springer-Verlag, Berlin, Heidelberg, 1987. MR 882921 (88m:03003)
  • [3] R. I. Soare and M. Stob, Relative recursive enumerability, Proceedings of the Herbrand Symposium Logic Colloquium 1981, (J. Stern, ed.), North-Holland, Amsterdam, 1982, pp. 299-324. MR 757037 (86b:03050)

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DOI: https://doi.org/10.1090/S0002-9939-1989-0937847-4
Article copyright: © Copyright 1989 American Mathematical Society

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