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A minimal pair of recursively enumerable degrees

Published online by Cambridge University Press:  12 March 2014

C. E. M. Yates
C. E. M. Yates*
Affiliation:
Cornell University, Institute for Advanced Study
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Extract

Our principal result is that there exist two incomparable recursively enumerable degrees whose greatest lower bound in the upper semilattice of degrees is 0. This was conjectured by Sacks [5]. As a secondary result, we prove that on the other hand there exists a recursively enumerable degree a < 0(1) such that for no non-zero recursively enumerable degree b is 0 the greatest lower bound of a and b.

The proof of the main theorem involves a method that we have developed elsewhere [8] to deal with situations in which a partial recursive functional may interfere infinitely often with an opposed requirement of lower priority.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 31 , Issue 2 , June 1966 , pp. 159 - 168
Copyright
Copyright © Association for Symbolic Logic 1966

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References

REFERENCES

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