Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-22T06:46:32.037Z Has data issue: false hasContentIssue false
  • English
  • Français

The strong homogeneity conjecture

Published online by Cambridge University Press:  12 March 2014

L. Feiner
L. Feiner*
Affiliation:
State University of New York at Stony Brook
Get access Rights & Permissions [Opens in a new window]

Extract

The strong homogeneity conjecture asserts that, for any Turing degree, a, there is a jump preserving isomorphism from the upper semilattice of degrees to the upper semilattice of degrees above a. Rogers [3, p. 261] states that this problem is open and notes that its truth would simplify many proofs about degrees. It is, in fact, false. More precisely, let 0 be the smallest degree and let 0(n) be the nth iterated jump of 0, as defined in [3, pp. 254–256].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 35 , Issue 3 , September 1970 , pp. 375 - 377
Copyright
Copyright © Association for Symbolic Logic 1971

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.)

References

[1]Feiner, L., Degrees of non-recursive presentability, in preparation.Google Scholar
[2]Hugill, D., Initial segments of Turing degrees, Proceedings of the London Mathematical Society, vol. 19 (1969), pp. 1–15.CrossRefGoogle Scholar
[3]Rogers, H., The theory of recursive functions and effective computability, McGraw-Hill, New York, 1967.Google Scholar
[4]Yates, C., A survey of degrees (to appear).Google Scholar