We construct an incomplete 3-c.e. enumeration degree which is maximal among the n-c.e, enumeration degrees for every n with $3 \leq n \leq \omega$. Consequently the n-c.e. enumeration degrees are not dense for any such n. We show also that no low n-c.e, e-degree can be maximal among the n-c.e. e-degrees, for $2 \leq n \leq \omega$.
Cooper, S.B., Li, A., Sorbi, A., Yang, Y. (2003). There exists a maximal 3-c.e. enumeration degree. ISRAEL JOURNAL OF MATHEMATICS, 137, 285-320 [10.1007/BF02785966].
There exists a maximal 3-c.e. enumeration degree
SORBI, ANDREA;
2003-01-01
Abstract
We construct an incomplete 3-c.e. enumeration degree which is maximal among the n-c.e, enumeration degrees for every n with $3 \leq n \leq \omega$. Consequently the n-c.e. enumeration degrees are not dense for any such n. We show also that no low n-c.e, e-degree can be maximal among the n-c.e. e-degrees, for $2 \leq n \leq \omega$.
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https://hdl.handle.net/11365/9154