Geodesic
On a Class of Complete Simple Sets
Canadian mathematical bulletin, Tome 8 (1965) no. 1, pp. 33-37

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Since the solution of Post' s Problem by Friedberg and Muchnik, a good deal of abstract knowledge about the semilattice of recursively enumerable degrees has been developed, especially in recent papers of G. E. Sacks. In this note, we show that one specific class of simple sets contains only sets of degree 0'; no contribution to the general theory is claimed. One of the sets belonging to the special class considered is the original simpie-but-not-hypersimple S of Post [1]. According to information received from Sacks, J. R. Myhill gave a proof, in 1953, of the completeness of S. However, as far as we know, Myhill' s proof (presented in a seminar) does not exist in published form. 
McLaughlin, T. G. On a Class of Complete Simple Sets. Canadian mathematical bulletin, Tome 8 (1965) no. 1, pp. 33-37. doi: 10.4153/CMB-1965-006-2
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