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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Jumps of orderings

Authors: C. J. Ash, C. G. Jockusch and J. F. Knight
Journal: Trans. Amer. Math. Soc. 319 (1990), 573-599
MSC: Primary 03D30
MathSciNet review: 955487
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Abstract: Here it is shown that for each recursive ordinal $ \alpha \geqslant 2$ and each Turing degree $ {\mathbf{d}} > {{\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 $th jumps of degrees of copies of $ {\mathbf{A}}$ has no least element.

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