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The Friedberg-Muchnik Theorem Re-Examined

Published online by Cambridge University Press:  20 November 2018

Robert I. Soare
Robert I. Soare*
Affiliation:
University of Illinois at Chicago Circle, Chicago, Illinois
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In the well-known solution to Post's problem, Friedberg [1] and Muchnik [13] each constructed a pair of incomparable recursively enumerable (r.e.) degrees a and b. Subsequently, Sacks [15, p. 81] constructed r.e. degrees c and d such that c ∪ d = 0’ and C’ = d’ = 0'. Lachlan showed [7, p. 69] that such degrees c, d could have no greatest lower bound in the upper semilattice of r.e. degrees. We show that the original Friedberg-Muchnik degrees a, b automatically satisfy Sack's conditions and hence witness that the upper semi-lattice of r.e. degrees is not a lattice.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 6 , December 1972 , pp. 1070 - 1078
Copyright
Copyright © Canadian Mathematical Society 1972

References

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