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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The quotient semilattice of the recursively enumerable degrees modulo the cappable degrees


Author: Steven Schwarz
Journal: Trans. Amer. Math. Soc. 283 (1984), 315-328
MSC: Primary 03D25; Secondary 03D30
MathSciNet review: 735425
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Abstract: In this paper, we investigate the quotient semilattice $ \underline R /\underline M $ of the r.e. degrees modulo the cappable degrees. We first prove the $ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{R} /\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{M} $ counterpart of the Friedberg-Muchnik theorem. We then show that minimal elements and minimal pairs are not present in $ \underline R /\underline M $. We end with a proof of the $ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{R} /\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{M} $ counterpart to Sack's splitting theorem.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0735425-3
PII: S 0002-9947(1984)0735425-3
Article copyright: © Copyright 1984 American Mathematical Society