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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Orderings with $ \alpha$th jump degree $ {\bf0}\sp {(\alpha)}$


Authors: Rodney Downey and Julia F. Knight
Journal: Proc. Amer. Math. Soc. 114 (1992), 545-552
MSC: Primary 03D45; Secondary 03C57, 03D30
MathSciNet review: 1065942
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Abstract: This paper completes an investigation of "jumps" of orderings. The last few cases are given in the proof that for each recursive ordinal $ \alpha \geq 1$ and for each Turing degree $ {\mathbf{d}} \geq {{\mathbf{0}}^{(\alpha )}}$, there is a linear ordering $ {\mathbf{A}}$ such that $ {\mathbf{d}}$ is least among the $ \alpha $th jumps of degrees of (open diagrams of) isomorphic copies of $ {\mathbf{A}}$, and for $ \beta < \alpha $, the set of $ \beta $ jumps of degrees of copies of $ {\mathbf{A}}$ has no least element.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1065942-0
Article copyright: © Copyright 1992 American Mathematical Society