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Discontinuity of Cappings in the Recursively Enumerable Degrees and Strongly Nonbranching Degrees
Author(s) -
AmbosSpies Klaus,
Decheng Ding
Publication year - 1994
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19940400302
Subject(s) - mathematics , recursively enumerable language , discontinuity (linguistics) , combinatorics , degree (music) , pure mathematics , mathematical physics , physics , mathematical analysis , acoustics
We construct an r. e. degree a which possesses a greatest a‐minimal pair b 0 , b 1 , i.e., r. e. degrees b 0 and b 1 such that b 0 , b 1 < a, b 0 ∩ b 1 = a, and, for any other pair c 0 , c 1 with these properties, c 0 ≤ b i and c 1 ≤ b 1‐ 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.