Discontinuity of cappings in the recursively enumerable degrees and strongly nonbranching degrees
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 n...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
1994
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| In: |
Mathematical logic quarterly
Year: 1994, Volume: 40, Issue: 3, Pages: 287-317 |
| ISSN: | 1521-3870 |
| DOI: | 10.1002/malq.19940400302 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1002/malq.19940400302 Verlag, lizenzpflichtig, Volltext: https://onlinelibrary.wiley.com/doi/abs/10.1002/malq.19940400302 
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| Author Notes: | Klaus Ambos-Spies, Ding Decheng |
| Summary: | 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. |
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| Item Description: | Gesehen am 31.05.2023 |
| Physical Description: | Online Resource |
| ISSN: | 1521-3870 |
| DOI: | 10.1002/malq.19940400302 |