Journal of Symbolic Logic 45 (2):204-220 (1980)

Authors
Harold Hodes
Cornell University
Abstract
Where $\underline{a}$ is a Turing degree and ξ is an ordinal $ , the result of performing ξ jumps on $\underline{a},\underline{a}^{(\xi)}$ , is defined set-theoretically, using Jensen's fine-structure results. This operation appears to be the natural extension through $(\aleph_1)^{L^\underline{a}}$ of the ordinary jump operations. We describe this operation in more degree-theoretic terms, examine how much of it could be defined in degree-theoretic terms and compare it to the single jump operation
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DOI 10.2307/2273183
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References found in this work BETA

Set Theory and the Continuum Hypothesis.Kenneth Kunen - 1966 - Journal of Symbolic Logic 35 (4):591-592.
Gaps in the Contructable Universe.W. Marek & M. Srebrny - 1974 - Annals of Mathematical Logic 6 (3-4):359-394.
Uniform Upper Bounds on Ideals of Turing Degrees.Harold T. Hodes - 1978 - Journal of Symbolic Logic 43 (3):601-612.

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Citations of this work BETA

A Non-Inversion Theorem for the Jump Operator.Richard A. Shore - 1988 - Annals of Pure and Applied Logic 40 (3):277-303.
Mathematical Definability.Theodore A. Slaman - 1998 - In H. G. Dales & Gianluigi Oliveri (eds.), Truth in Mathematics. Oxford University Press, Usa. pp. 233.

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