Discontinuity of Cappings in the Recursively Enumerable Degrees and Strongly Nonbranching Degrees
Klaus Ambos‐Spies, Ding Decheng · Mathematical logic quarterly · 1994
Abstract We construct an r. e. degree a which possesses a greatest a‐minimal pair b0, b1, i.e., r. e. degrees b0 and b1 such that b0, b1 < a, b0 ∩ b1 = a, and, for any other pair c0, c1 with these properties, c0 ≤ bi and c1 ≤ b1‐i for some i ≤ 1. By extending this result, we show that there are strongly nonbranching degrees which are not strongly noncappable. Finally, by introducing a new genericity concept for r. e. sets, we prove a jump theorem for the strongly nonbranching and strongly noncappable r. e. degrees. Mathematics Subject Classification: 03D25.