2-Minimality, jump classes and a note on natural definability

Annals of Pure and Applied Logic 165 (2):724-741 (2014)
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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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10.1016/j.apal.2013.10.005

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References found in this work

Double Jumps of Minimal Degrees.Carl G. Jockusch & David B. Posner - 1978 - Journal of Symbolic Logic 43 (4):715 - 724.
Minimal degrees and the jump operator.S. B. Cooper - 1973 - Journal of Symbolic Logic 38 (2):249-271.
Direct and local definitions of the Turing jump.Richard A. Shore - 2007 - Journal of Mathematical Logic 7 (2):229-262.

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