Hostname: page-component-7f64f4797f-vhqbp Total loading time: 0 Render date: 2025-11-04T04:53:40.498Z Has data issue: false hasContentIssue false
  • English
  • Français

An almost deep degree

Published online by Cambridge University Press:  12 March 2014

Peter Cholak ,
Marcia Groszek  and
Theodore Slaman
Peter Cholak
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA, E-mail: peter.cholak.1@nd.edu
Marcia Groszek
Affiliation:
Department of Mathematics, Dartmouth College Hanover, NH 03755, USA, E-mail: marcia.groszek@dartmouth.edu
Theodore Slaman
Affiliation:
Department of Mathematics, University of California – Berkeley, Berkeley, CA 94720., USA, E-mail: slaman@math.berkeley.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We show there is a non-recursive r.e. set A such that if W is any low r.e. set. then the join W ⊕ A is also low. That is. A is “almost deep”. This answers a question of Joekusch. The almost deep degrees form an definable ideal in the r.e. degrees (with jump.)

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 2 , June 2001 , pp. 881 - 901
Copyright
Copyright © Association for Symbolic Logic 2001

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.)

Article purchase

Temporarily unavailable

References

REFERENCES

[1]Bickford, M. and Mills, C. F., Lowness properties of r.e. sets, to appear.Google Scholar
[2]Lempp, Steffen and Lerman, Manuel, The decidability of the existential theory of the poset of recursively enumerable degrees with jump relations, Advances in Mathematics, vol. 120 (1996), pp. 1–142.CrossRefGoogle Scholar
[3]Lempp, Steffen and Slaman, Theodore A., A limit on relative genericity in the recursively enumerable sets, this Journal, vol. 54 (1989), pp. 376–395.Google Scholar