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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
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.


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