Bounding and nonbounding minimal pairs in the enumeration degrees. (English) Zbl 1093.03029
In this very interesting paper it is proved that: 1) Every nonzero \(\Delta^0_2\) e-degree bounds a minimal pair. Every nonzero \(\Delta^0_2\) s-degree bounds a minimal pair of s-degrees. 2) There exists a nonzero \(\Sigma^0_2\) e-degree which bounds no minimal pairs. There exists a nonzero \(\Sigma^0_2\) s-degree that does not bound any minimal pair of s-degrees.
Reviewer: Roland Sh. Omanadze (Tbilisi)
MSC:
| 03D30 | Other degrees and reducibilities in computability and recursion theory |
| 03D25 | Recursively (computably) enumerable sets and degrees |
References:
| [1] | Recursion Theory Week, Oberwolfach 1989 1432 pp 57– (1990) |
| [2] | DOI: 10.1002/malq.19870330608 · Zbl 0646.03037 · doi:10.1002/malq.19870330608 |
| [3] | Partial degrees and the density problem 47 pp 854– (1982) |
| [4] | DOI: 10.1023/A:1022660222520 · doi:10.1023/A:1022660222520 |
| [5] | l-genericity in the enumeration degrees pp 878– (1988) |
| [6] | On minimal pairs of enumeration degrees 50 pp 983– (1985) · Zbl 0615.03031 |
| [7] | Recursion Theory and Complexity pp 157– (1999) |
| [8] | Bounding minimal pairs 44 pp 626– (1979) |
| [9] | DOI: 10.1002/malq.19590050703 · Zbl 0108.00602 · doi:10.1002/malq.19590050703 |
| [10] | Recursively Enumerable Sets and Degrees (1987) |
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