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An Algebraic Decomposition of the Recursively Enumerable Degrees and the Coincidence of Several Degree Classes with the Promptly Simple Degrees
1984
Transactions of the American Mathematical Society
We specify a definable decomposition of the upper semilattice of recursively enumerable (r.e.) degrees R as the disjoint union of an ideal M and a strong filter NC. The ideal M consists of 0 together with all degrees which are parts of r.e. minimal pairs, and thus the degrees in NC are called noncappable degrees. Furthermore, NC coincides with five other apparently unrelated subclasses of R: ENC, the effectively noncappable degrees; PS, the degrees of promptly simple sets; LC, the r.e. degrees
doi:10.2307/1999525
fatcat:7b4ipsjzs5hbxgobaqklcbryby