Abstract
We prove that no subclass of the \(\Sigma^0_2\) enumeration degrees containing the nonzero 3-c.e. enumeration degrees can be cupped to 0 e ′ by a single incomplete \(\Sigma^0_2\) enumeration degree.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Cooper, S.B.: Partial degrees and the density problem. J. Symb. Log. 47, 854–859 (1982)
Cooper, S.B.: Partial Degrees and the density problem. part 2: the enumeration degrees of the Σ 2 sets are dense. J. Symb. Log. 49, 503–513 (1984)
Cooper, S.B.: Enumeration reducibility, nondeterminitsic computations and relative computability of partial functions. In: Recursion Theory Week, Oberwolfach 1989. Lecture Notes in Mathematics, vol. 1432, pp. 57–110 (1990)
Cooper, S.B.: Computability Theory. Chapman & Hall/CRC Mathematics, Boca Raton (2004)
Cooper, S.B.: On a theorem of C.E.M. Yates, handwritten notes (1973)
Cooper, S.B., Sorbi, A., Yi, X.: Cupping and noncupping in the enumeration degrees of Σ 2 0 sets. Ann. Pure Appl. Logic 82, 317–342 (1996)
Jockusch Jr., C.G.: Semirecursive sets and positive reducibility. Trans.Amer.Math.Soc. 131, 420–436 (1968)
Lachlan, A.H., Shore, R.A.: The n-rea enumeration degrees are dense. Arch. Math. Logic 31, 277–285 (1992)
Posner, D., Robinson, R.: Degrees joining to 0′. J. Symbolic Logic 46, 714–722 (1981)
Soare, R.I.: Recursively enumerable sets and degrees. Springer, Heidelberg (1987)
Soskova, M., Wu, G.: Cupping Δ 0 2 enumeration degrees to 0′. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds.) CiE 2007. LNCS, vol. 4497, pp. 727–738. Springer, Heidelberg (2007)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Soskova, M.I. (2008). Cupping Classes of \(\Sigma^0_2\) Enumeration Degrees. In: Beckmann, A., Dimitracopoulos, C., Löwe, B. (eds) Logic and Theory of Algorithms. CiE 2008. Lecture Notes in Computer Science, vol 5028. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69407-6_59
Download citation
DOI: https://doi.org/10.1007/978-3-540-69407-6_59
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69405-2
Online ISBN: 978-3-540-69407-6
eBook Packages: Computer ScienceComputer Science (R0)