×

Degrees coded in jumps of orderings. (English) Zbl 0633.03038

Jockusch asked whether for any positive integer n, there exist orderings \({\mathfrak A}\) having nth jump degree but not having kth jump degree for \(k<n\). The paper offers the following results: i) The only first jump possible for an ordering is \(0'\). ii) For each positive integer n, there is an ordering \({\mathfrak A}_ n\) such that \({\mathfrak A}_ n\) has \((2n+2)nd\) jump degree and does not have \((n+1)st\) jump degree.
Reviewer: C.Calude

MSC:

03D30 Other degrees and reducibilities in computability and recursion theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1007/BF02757141 · Zbl 0304.02025
[2] Linear orderings (1982) · Zbl 0488.04002
[3] Degrees of structures 46 pp 723– (1981)
[4] Fundamenta Mathematicae 56 pp 117– (1964)
[5] Contributions to mathematical logic (colloquium, Hannover, 1966) pp 189– (1968)
[6] Transactions of the American Mathematical Society 173 pp 33– (1972) · Zbl 0247.00014
[7] Proceedings of the London Mathematical Society 25 pp 586– (1972)
[8] Proceedings of the Herbrand symposium, (Marseille, 1981 pp 233– (1982)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.