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Isolation and the high/low hierarchy

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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 &ndash; d.c.e. degree &ndash; Isolation &ndash; 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.

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Authors and Affiliations

  1. Department of Mathematics Ulyanovsk State University, 432700 Ulyanovsk, Russia. e-mail: ishm@vens.ru, , , , , , RU

    Shamil Ishmukhametov

  2. School of Mathematical and Computing Sciences Victoria University of Wellington, New Zealand. e-mail: wu@mcs.vuw.ac.nz, , , , , , NZ

    Guohua Wu

Authors
  1. Shamil Ishmukhametov
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  2. Guohua Wu
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Additional information

Received: 31 January 2001 / Published online: 25 February 2002

RID=""

ID="" <E5>Mathematics Subject Classification (2000):</E5> 03D25, 03D30, 03D35

RID=""

ID="" <E5>Key words or phrases:</E5> Computably enumerable set &ndash; d.c.e. degree &ndash; Isolation &ndash; 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.

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Ishmukhametov, S., Wu, G. Isolation and the high/low hierarchy . Arch. Math. Logic 41 , 259 –266 (2002). https://doi.org/10.1007/s001530100111

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  • DOI: https://doi.org/10.1007/s001530100111

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