论文信息 - Isolation and the high/low hierarchy

Isolation and the high/low hierarchy

Abstract Say that a d.c.e. degree d is isolated by a c.e. degree b, if b<d and any c.e. degree c below d is also below b, namely, b is the largest c.e. degree below d. Wu proved that there is a high d.c.e. degree d isolated by a low2 c.e. degree b. In this paper, we improve this result by making b low, not merely low2. RID=""ID="" <E5>Mathematics Subject Classification (2000):</E5> 03D25, 03D30, 03D35 RID=""ID="" <E5>Key words or phrases:</E5> Computably enumerable set – d.c.e. degree – Isolation – High/low hierarchy RID=""ID="" Ishmukhametov's research is supported by RFBR grant 01-01-00733, and Wu's research is supported by the Marsden Fund of New Zealand. Wu would like to thank his supervisor, Prof. Rod Downey, for his many helpful suggestions and comments.

Guohua Wu | Shamil Ishmukhametov

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