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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: [email protected]
Marcia Groszek
Affiliation:
Department of Mathematics, Dartmouth College Hanover, NH 03755, USA, E-mail: [email protected]
Theodore Slaman
Affiliation:
Department of Mathematics, University of California – Berkeley, Berkeley, CA 94720., USA, E-mail: [email protected]
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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.)

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

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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