Annals of Pure and Applied Logic 165 (2):724-741 (2014)

Abstract
We show that there is a generalized high degree which is a minimal cover of a minimal degree. This is the highest jump class one can reach by finite iterations of minimality. This result also answers an old question by Lerman
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DOI 10.1016/j.apal.2013.10.005
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References found in this work BETA

Direct and Local Definitions of the Turing Jump.Richard A. Shore - 2007 - Journal of Mathematical Logic 7 (2):229-262.
Characterizing the Join-Irreducible Medvedev Degrees.Paul Shafer - 2011 - Notre Dame Journal of Formal Logic 52 (1):21-38.
Double Jumps of Minimal Degrees.Carl G. Jockusch & David B. Posner - 1978 - Journal of Symbolic Logic 43 (4):715 - 724.

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