Abstract.
The partial ordering of Medvedev reducibility restricted to the family of Π0 1 classes is shown to be dense. For two disjoint computably enumerable sets, the class of separating sets is an important example of a Π0 1 class, which we call a ``c.e. separating class''. We show that there are no non-trivial meets for c.e. separating classes, but that the density theorem holds in the sublattice generated by the c.e. separating classes.
Article PDF
Avoid common mistakes on your manuscript.
References
Cenzer, D.: Π0 1 classes in computability theory, Handbook of Computability Theory, Studies in Logic and the Foundations of Mathematics, 140, 37–85 (1999)
Cenzer, D., Remmel, J.: Index sets for Π0 1 classes, Ann. Pure and Appl. Logic 43, 3–61 (1998)
Hinman, P.G.: Recursion-Theoretic Hierarchies. Perspectives in Mathematical Logic, Springer-Verlag, Berlin (1978)
Jockusch, C., Soare, R.: Π0 1 classes and degrees of theories. Trans. Amer. Math. Soc. 173, 33–56 (1972)
Medvedev, Yu.: Degrees of difficulty of the mass problem. Dok. Akad. Nauk SSSR 104, 501–504 (1955)
Odifreddi, P.: Classical Recursion Theory. North-Holland (1989)
Simpson, S.: Π0 1 Sets and Models of WKL 0, to appear in Reverse Mathematics 2001, ed. S. Simpson
Binns, S., Simpson, S.: Medvedev and Muchnik Degrees of Nonempty Π0 1 Subsets of 2ω, preprint, May 2001
Sorbi, A.: The Medvedev lattice of degrees of difficulty, in Computability, Enumerability, Unsolvability, London Math. Soc. Lecture Notes 224, Cambridge University Press, Cambridge 289–312 (1996)
Author information
Authors and Affiliations
Corresponding author
Additional information
Mathematics Subject Classification (2000): 03D30, 03D25
Rights and permissions
About this article
Cite this article
Cenzer, D., Hinman, P. Density of the Medvedev lattice of Π0 1 classes. Arch. Math. Logic 42, 583–600 (2003). https://doi.org/10.1007/s00153-002-0166-7
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00153-002-0166-7