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An almost deep degree

  • Peter Cholak (a1), Marcia Groszek (a2) and Theodore Slaman (a3)

We show there is a non-recursive r.e. set A such that if W is any low r.e. set. then the join WA 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.)

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[1]Bickford M. and Mills C. F., Lowness properties of r.e. sets, to appear.
[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. 1142.
[3]Lempp Steffen and Slaman Theodore A., A limit on relative genericity in the recursively enumerable sets, this Journal, vol. 54 (1989), pp. 376395.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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