Abstract
We construct a \({\Sigma^0_2}\) e-degree which is both high and noncuppable. Thus demonstrating the existence of a high e-degree whose predecessors are all properly \({\Sigma^0_2}\).
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Cooper S.B.: Partial degrees and the density problem. Part 2, The enumeration degrees of Σ2 sets are dense. J Symb Log 49, 503–513 (1984)
Cooper S.B., Sorbi A., Yi X.: Cupping and noncupping in the enumeration degrees of \({\Sigma^0_2}\) sets. Ann. Pure Appl. Log. 82, 317–342 (1996)
Friedberg R.M., Rogers H. Jr.: Reducibility and completeness for sets of intergers. Z. Math. Log. Grundl. Math. 5, 161–175 (1959)
McEvoy, K.: The Structure of the Enumeration Degrees. Ph.D. thesis, Leeds University (1984)
McEvoy K.: Jumps of quasi-minimal enumeration degrees. J. Symb. Log. 50, 839–848 (1985)
McEvoy K., Cooper S.B.: On minimal pairs of enumeration degrees. J. Symb. Log. 50, 983–1001 (1985)
Shore, R., Sorbi, A.: Jumps of \({\Sigma^0_2}\)-high e-degrees and properly \({\Sigma^0_2}\) e-degrees. In: Arslanov, M.M., Lempp, S. (eds.) Recursion Theory and Complexity. De Gruyter series in logic and its applications, vol. 2, pp. 157–172. prodeedings Kazan. De Gruyter, Berlin, New York (1999)
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Giorgi, M.B. A high noncuppable \({\Sigma^0_2}\) e-degree. Arch. Math. Logic 47, 181–191 (2008). https://doi.org/10.1007/s00153-006-0021-3
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DOI: https://doi.org/10.1007/s00153-006-0021-3