The Quotient Semilattice of the Recursively Enumerable Degrees Modulo the Cappable Degrees
Steven Schwarz · Transactions of the American Mathematical Society · 1984
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 $\underline {R} /\underline {M}$ 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 $\underline {R} /\underline {M}$ counterpart to Sack’s splitting theorem.