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Isolation and lattice embeddings

Published online by Cambridge University Press:  12 March 2014

Guohua Wu
Guohua Wu*
Affiliation:
School of Mathematical and Computing Sciences, Victoria University, of Wellington, P.O. Box 600, Wellington, New Zealand, E-mail: wu@mcs.vuw.ac.nz
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Abstract

Say that (a, d) is an isolation pair if a is a c.e. degree, d is a d.c.e. degree, a < d and a bounds all c.e. degrees below d. We prove that there are an isolation pair (a, d) and a c.e. degree c such that c is incomparable with a, d, and c cups d to o′, caps a to o. Thus, {o, c, d, o′} is a diamond embedding, which was first proved by Downey in [9]. Furthermore, combined with Harrington-Soare continuity of capping degrees, our result gives an alternative proof of N5 embedding.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 3 , September 2002 , pp. 1055 - 1064
Copyright
Copyright © Association for Symbolic Logic 2002

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References

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