Decomposition of recursively enumerable degrees

Decomposition of recursively enumerable degrees
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by A. H. Lachlan PDF

Proc. Amer. Math. Soc. 79 (1980), 629-634 Request permission

It is shown that any nonzero recursively enumerable degree can be expressed as the join of two distinct such degrees having a greatest lower bound.

References

A. H. Lachlan, Lower bounds for pairs of recursively enumerable degrees, Proc. London Math. Soc. (3) 16 (1966), 537–569. MR 204282, DOI 10.1112/plms/s3-16.1.537
A. H. Lachlan, The priority method for the construction of recursively enumerable sets, Cambridge Summer School in Mathematical Logic (Cambridge, 1971) Lecture Notes in Math., Vol. 337, Springer, Berlin, 1973, pp. 299–310. MR 0335247
Gerald E. Sacks, On the degrees less than 0′, Ann. of Math. (2) 77 (1963), 211–231. MR 146078, DOI 10.2307/1970214

The generalized diamond theorem

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Robert I. Soare, Recursively enumerable sets and degrees, Bull. Amer. Math. Soc. 84 (1978), no. 6, 1149–1181. MR 508451, DOI 10.1090/S0002-9904-1978-14552-2
C. E. M. Yates, A minimal pair of recursively enumerable degrees, J. Symbolic Logic 31 (1966), 159–168. MR 205851, DOI 10.2307/2269807