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A high c.e. degree which is not the join of two minimal degrees

Published online by Cambridge University Press:  12 March 2014

Matthew B. Giorgi
Matthew B. Giorgi*
Affiliation:
14 Swan Hill Cottages, Aylesbury Road, Cuddington, Buckinghamshire, HP18 0BE, UK. E-mail: matthewgiorgi@hotmail.com
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Abstract

We construct a high c.e. degree which is not the join of two minimal degrees and so refute Posner's conjecture that every high c.e. degree is the join of two minimal degrees. Additionally, the proof shows that there is a high c.e. degree a such that for any splitting of a into degrees b and c one of these degrees bounds a 1-generic degree.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 4 , December 2010 , pp. 1339 - 1358
Copyright
Copyright © Association for Symbolic Logic 2010

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References

REFERENCES

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