Bounding nonsplitting enumeration degrees. (English) Zbl 1131.03019

Ahmad has shown the existence of nonzero \(\Sigma^0_2\) enumeration degrees, i.e., enumeration degrees below \({\mathbf 0}_e'\) that are nonsplitting. The present paper shows that, in fact, every nonzero \(\Sigma^0_2\) enumeration degree lies above such a degree.


03D30 Other degrees and reducibilities in computability and recursion theory
Full Text: DOI Euclid


[1] DOI: 10.1023/A:1022660222520
[2] DOI: 10.1002/malq.19980440402 · Zbl 0926.03045
[3] Embedding the diamond in the {\(\Sigma\)}2 enumeration degrees 56 pp 195– (1991)
[4] Recursively enumerable sets and degrees (1987)
[5] Partial degrees and the density problem. II, The enumeration degrees of the {\(\Sigma\)}2 sets are dense 49 pp 503– (1984) · Zbl 0574.03027
[6] DOI: 10.2307/1970214 · Zbl 0118.25104
[7] Jumps of quasiminimal enumeration degrees 50 pp 839– (1985)
[8] DOI: 10.1007/BF01794984 · Zbl 0848.03023
[9] Proceedings of the London Mathematical Society. Third Series 16 pp 537– (1966)
[10] On minimal pairs of enumeration degrees 50 pp 983– (1985) · Zbl 0615.03031
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.