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The Quotient Semilattice of the Recursively Enumerable Degrees Modulo the Cappable Degrees

1984
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Transactions of the American Mathematical Society
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In this paper, we investigate the quotient semilattice R/M of the r.e. degrees modulo the cappable degrees. We first prove the R/M counterpart of the Friedberg-Muchnik theorem. We then show that minimal elements and minimal pairs are not present in R/M. We end with a proof of the R/M counterpart to Sack's splitting theorem. 0. Introduction. The set of all r.e. degrees is made into an upper semilattice (with 0 and 1) in a natural way: namely, the reducibility relation between r.e. sets induces a

doi:10.2307/2000006
fatcat:ms3vfscxfnb5bh3jzrxhbojvrm