The jump classes of minimal covers

Lewis-Pye, A. (2006). The jump classes of minimal covers. In Beckmann, A., Berger, U., Löwe, B. & Tucker, J. V. (Eds.), Logical Approaches to Computational Barriers: Second Conference on Computability in Europe, Cie 2006, Swansea, Uk, June 30-July (pp. 307-318). Springer Berlin / Heidelberg. https://doi.org/10.1007/11780342_33
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We work in D[<0′] . Given the jump class of any (Turing) degree a, the jump classes of the minimal covers of a is a matter which is entirely settled unless a is high 2. We show that there exists a c.e. degree which is high 2 with no high 1 minimal cover.

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