Journal of Symbolic Logic

On the jump classes of noncuppable enumeration degrees

Charles M. Harris

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We prove that for every Σ02 enumeration degree b there exists a noncuppable Σ02 degree a > 0e such that b'c a' and a''c b''. This allows us to deduce, from results on the high/low jump hierarchy in the local Turing degrees and the jump preserving properties of the standard embedding ι : 𝒟T → 𝒟e, that there exist Σ02 noncuppable enumeration degrees at every possible—i.e., above low1—level of the high/low jump hierarchy in the context of 𝒟e.

Article information

Source
J. Symbolic Logic, Volume 76, Issue 1 (2011), 177-197.

Dates
First available in Project Euclid: 4 January 2011

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1294170994

Digital Object Identifier
doi:10.2178/jsl/1294170994

Mathematical Reviews number (MathSciNet)
MR2791342

Zentralblatt MATH identifier
1215.03056

Citation

Harris, Charles M. On the jump classes of noncuppable enumeration degrees. J. Symbolic Logic 76 (2011), no. 1, 177--197. doi:10.2178/jsl/1294170994. https://projecteuclid.org/euclid.jsl/1294170994


Export citation