Jumps of orderings
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- by C. J. Ash, C. G. Jockusch and J. F. Knight
- Trans. Amer. Math. Soc. 319 (1990), 573-599
- DOI: https://doi.org/10.1090/S0002-9947-1990-0955487-0
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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.References
- C. J. Ash, Recursive labelling systems and stability of recursive structures in hyperarithmetical degrees, Trans. Amer. Math. Soc. 298 (1986), no. 2, 497–514. MR 860377, DOI 10.1090/S0002-9947-1986-0860377-7 C. J. Ash and J. F. Knight, Pairs of structures, Ann. Pure Appl. Logic (to appear).
- 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 L. Harrington, Building nonstandard models of Peano arithmetic, handwritten notes, 1979. C. G. Jockusch and R. I. Soare, Degrees of linear orderings not isomorphic to recurisve ones, preprint.
- Julia F. Knight, Effective construction of models, Logic colloquium ’84 (Manchester, 1984) Stud. Logic Found. Math., vol. 120, North-Holland, Amsterdam, 1986, pp. 105–119. MR 861421, DOI 10.1016/S0049-237X(08)70459-2
- Julia F. Knight, Degrees coded in jumps of orderings, J. Symbolic Logic 51 (1986), no. 4, 1034–1042. MR 865929, DOI 10.2307/2273915 —, Degrees of models with prescribed Scott set, Classification Theory: Proc., Chicago, 1985 (J. Baldwin, ed.), Lecture Notes in Math., vol. 1292, Springer-Verlag, 1988, pp. 182191.
- J. F. Knight, A metatheorem for constructions by finitely many workers, J. Symbolic Logic 55 (1990), no. 2, 787–804. MR 1056389, DOI 10.2307/2274665
- Manuel Lerman, On recursive linear orderings, Logic Year 1979–80 (Proc. Seminars and Conf. Math. Logic, Univ. Connecticut, Storrs, Conn., 1979/80) Lecture Notes in Math., vol. 859, Springer, Berlin, 1981, pp. 132–142. MR 619867
- John M. Macintyre, Transfinite extensions of Friedberg’s completeness criterion, J. Symbolic Logic 42 (1977), no. 1, 1–10. MR 491099, DOI 10.2307/2272313
- David Marker, Degrees of models of true arithmetic, Proceedings of the Herbrand symposium (Marseilles, 1981) Stud. Logic Found. Math., vol. 107, North-Holland, Amsterdam, 1982, pp. 233–242. MR 757032, DOI 10.1016/S0049-237X(08)71887-1
- 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
Bibliographic Information
- © Copyright 1990 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 319 (1990), 573-599
- MSC: Primary 03D30
- DOI: https://doi.org/10.1090/S0002-9947-1990-0955487-0
- MathSciNet review: 955487