Orderings with $\alpha$th jump degree $\textbf {0}^ {(\alpha )}$
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- by Rodney Downey and Julia F. Knight
- Proc. Amer. Math. Soc. 114 (1992), 545-552
- DOI: https://doi.org/10.1090/S0002-9939-1992-1065942-0
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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.References
- C. J. Ash, C. G. Jockusch Jr., and J. F. Knight, Jumps of orderings, Trans. Amer. Math. Soc. 319 (1990), no. 2, 573–599. MR 955487, DOI 10.1090/S0002-9947-1990-0955487-0
- C. J. Ash and J. F. Knight, Pairs of recursive structures, Ann. Pure Appl. Logic 46 (1990), no. 3, 211–234. MR 1049387, DOI 10.1016/0168-0072(90)90004-L
- Chris Ash, Julia Knight, Mark Manasse, and Theodore Slaman, Generic copies of countable structures, Ann. Pure Appl. Logic 42 (1989), no. 3, 195–205. MR 998606, DOI 10.1016/0168-0072(89)90015-8 C. G. Jockusch and R. I. Soare, Degrees of linear orderings not isomorphic to recursive ones, Ann. of Pure and Appl. Logic (to appear).
- Julia F. Knight, Degrees coded in jumps of orderings, J. Symbolic Logic 51 (1986), no. 4, 1034–1042. MR 865929, DOI 10.2307/2273915
- Linda Jean Richter, Degrees of structures, J. Symbolic Logic 46 (1981), no. 4, 723–731. MR 641486, DOI 10.2307/2273222
- Hartley Rogers Jr., Theory of recursive functions and effective computability, McGraw-Hill Book Co., New York-Toronto-London, 1967. MR 0224462
- Richard Watnick, A generalization of Tennenbaum’s theorem on effectively finite recursive linear orderings, J. Symbolic Logic 49 (1984), no. 2, 563–569. MR 745385, DOI 10.2307/2274189
Bibliographic Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 114 (1992), 545-552
- MSC: Primary 03D45; Secondary 03C57, 03D30
- DOI: https://doi.org/10.1090/S0002-9939-1992-1065942-0
- MathSciNet review: 1065942