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Wtt-degrees and T-degrees of r.e. sets

  • Michael Stob (a1)
Abstract
Abstract

We use some simple facts about the wtt-degrees of r.e. sets together with a construction to answer some questions concerning the join and meet operators in the r.e. degrees. The construction is that of an r.e. Turing degree a with just one wtt-degree in a such that a is the join of a minimal pair of r.e. degrees. We hope to illustrate the usefulness of studying the stronger reducibility orderings of r.e. sets for providing information about Turing reducibility.

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Calvin College, Grand Rapids, Michigan 49506
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L. Harrington and S. Shelah [1982], The undecidability of the recursively enumerable degrees, Bulletin (New Series) of the American Mathematical Society, vol. 6, pp. 7980.

C.G. Jockusch Jr. [1972], Degrees in which the recursive sets are uniformly recursive, Canadian Journal of Mathematics, vol. 24, pp. 10921099.

S. Kallibekov [1971], Index sets and degrees of unsolvability, Algebra i Logika, vol. 10, pp. 316326. (Russian)

A.H. Lachlan [1972], Embedding nondistributive lattices in the recursively enumerable degrees, Conference in Mathematical Logic—London '70, Lecture Notes in Mathematics, vol. 255, Springer-Verlag, Berlin, pp. 149177.

A.H. Lachlan [1975], A recursively enumerable degree which will not split over all lesser ones, Annals of Mathematical Logic, vol. 9, pp. 307365.

R.E. Ladner and L.P. Sasso [1975], The weak truth table degrees of recursively enumerable sets, Annals of Mathematical Logic, vol. 8, pp. 429448.

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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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