Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A remark on pseudojump operators

Authors: A. H. Lachlan and X. Yi
Journal: Proc. Amer. Math. Soc. 106 (1989), 489-491
MSC: Primary 03D25
MathSciNet review: 937847
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 03D25

Retrieve articles in all journals with MSC: 03D25

Additional Information

Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society