Abstract
In this paper we prove that every nonzero \(\Delta^0_2\) e-degree is cuppable to 0 e ′ by a 1-generic \(\Delta^0_2\) e-degree (so low and nontotal) and that every nonzero ω-c.e. e-degree is cuppable to 0 e ′ by an incomplete 3-c.e. e-degree.
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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: Ambos-Spies, K., Müller, G., Sacks, G.E (eds.) Recursion Theory Week, Oberwolfach 1989. Lecture Notes in Mathematics, vol. 1432, pp. 57–110. Springer, Heidelberg (1990)
Cooper, S.B.: Computability Theory, Chapman & Hall/CRC Mathematics, Boca Raton, FL, New York, London (2004)
Cooper, S.B., Copestake, C.S.: Properly Σ 2 enumeration degrees. Zeits. f. Math. Logik. u. Grundl. der Math. 34, 491–522 (1988)
Cooper, S.B., Sorbi, A., Yi, X.: Cupping and noncupping in the enumeration degrees of \(\Sigma_2^0\) sets. Ann. Pure Appl. Logic 82, 317–342 (1996)
Copestake, K.: 1-Genericity in the enumeration degrees below 0 e ′. In: Petkov, P.P. (ed.) Mathemcatical Logic, pp. 257–265. Plenum Press, New York (1990)
Copestake, K.: 1-Genericity enumeration Degrees. J. Symb. Log. 53, 878–887 (1988)
Gutteridge, L.: Some Results on Enumeration Reducibility, PhD thesis, Simon Fraser University (1971)
Soare, R.I.: Recursively enumerable sets and degrees. Springer, Berlin, Heidelberg, London, New York, Paris, Tokyo (1987)
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Soskova, M.I., Wu, G. (2007). Cupping \(\Delta_2^0\) Enumeration Degrees to 0 e ′. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds) Computation and Logic in the Real World. CiE 2007. Lecture Notes in Computer Science, vol 4497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73001-9_77
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DOI: https://doi.org/10.1007/978-3-540-73001-9_77
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