Mathematical Logic Quarterly 47 (1):3-34 (2001)

Abstract
A proof is given that 0′ is definable in the structure of the degrees of unsolvability. This answers a long-standing question of Kleene and Post, and has a number of corollaries including the definability of the jump operator
Keywords Computably enumerable degree  Turing definable  Jump operator  Turing degree  Computably enumerable set
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DOI 10.1002/1521-3870(200101)47:1
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Direct and Local Definitions of the Turing Jump.Richard A. Shore - 2007 - Journal of Mathematical Logic 7 (2):229-262.
Degree Structures: Local and Global Investigations.Richard A. Shore - 2006 - Bulletin of Symbolic Logic 12 (3):369-389.

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