Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2025-01-03T17:07:14.010Z Has data issue: false hasContentIssue false
  • English
  • Français

On initial segments of hyperdegrees1

Published online by Cambridge University Press:  12 March 2014

S. K. Thomason
S. K. Thomason*
Affiliation:
Simon Fraser University
Get access Rights & Permissions [Opens in a new window]

Extract

An initial segment of hyperdegrees is a set S of hyperdegrees such that whenever h ∈ S and k ≦ h then k ∈ S. The main results of this paper affirm the existence of initial segments having certain order types. In particular, if L is a finite distributive lattice then L is isomorphic to an initial segment of hyperdegrees [Theorem 1]; as a consequence the elementary theory of the ordering of hyperdegrees is recursively undecidable [Corollary 1].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 35 , Issue 2 , June 1970 , pp. 189 - 197
Copyright
Copyright © Association for Symbolic Logic 1970

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

1

This paper reports research supported in part by the National Research Council of Canada, Grant #A-4065.

References

[1]Gandy, R. O. and Sacks, G. E., A minimal hyperdegree, Fundamenta mathematicae, vol. 61 (1967), pp. 215–223.CrossRefGoogle Scholar
[2]Lachlan, A. H., Distributive initial segments of the degrees of unsolvability, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 14 (1968), pp. 457–472.CrossRefGoogle Scholar
[3]Rosenstein, Joseph G., Initial segments of degrees, Pacific journal of mathematics, vol. 24 (1968), pp. 163–172.CrossRefGoogle Scholar
[4]Spector, C., On degrees of recursive unsolvability, Annals of mathematics, vol. 64 (1956), pp. 581–592.CrossRefGoogle Scholar
[5]Thomason, S. K., The forcing method and the upper semi-lattice of hyperdegrees, Transactions of the American Mathematical Society, vol. 129 (1967), pp. 38–58.CrossRefGoogle Scholar