论文信息 - Relative Enumerability in the Difference Hierarchy

Relative Enumerability in the Difference Hierarchy

We show that the intersection of the class of 2-REA degrees with that of the co-r.e. degrees consists precisely of the class of d.r.e. degrees. We also include some applications and show that there is no natural generalization of this result to higher levels of the REA hierarchy. ?

Geoffrey LaForte | Theodore A. Slaman | Marat M. Arslanov

[1] Hilary Putnam,et al. Trial and error predicates and the solution to a problem of Mostowski , 1965, Journal of Symbolic Logic.

[2] Y. Ershov. A hierarchy of sets. I , 1968 .

[3] B. M. Fulk. MATH , 1992 .

[4] Steffen Lempp,et al. Weak density and cupping in the d-r.e. degrees , 1989 .

[5] Michael Stob,et al. Relative Recursive Enumerability , 1982 .

[6] Alistair H. Lachlan,et al. Lower Bounds for Pairs of Recursively Enumerable Degrees , 1966 .

[7] Peter G. Hinman,et al. Iterated relative recursive enumerability , 1994, Arch. Math. Log..

[8] Carl G. Jockusch,et al. Pseudo-jump operators. II: Transfinite iterations, hierarchies and minimal covers , 1984, Journal of Symbolic Logic.

[9] Richard A. Shore,et al. On isolating r.e. and isolated d-r.e. degrees , 1996 .

[10] Richard A. Shore,et al. Interpolating d-r.e. and REA degrees between r.e. degrees , 2003 .

[11] Geoffrey LaForte. The Isolated D. R. E. Degrees are Dense in the R. E. Degrees , 1996, Math. Log. Q..

[12] R. Soare. Recursively enumerable sets and degrees , 1987 .