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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: 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
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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

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