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Decomposition of recursively enumerable degrees

Author: A. H. Lachlan
Journal: Proc. Amer. Math. Soc. 79 (1980), 629-634
MSC: Primary 03D30
MathSciNet review: 572317
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Abstract: 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 [Enhancements On Off] (What's this?)

  • [1] A. H. Lachlan, Lower bounds for pairs of recursively enumerable degrees, Proc. London Math. Soc. 16 (1966), 537-569. MR 0204282 (34:4126)
  • [2] -, The priority method for the construction of recursively enumerable sets (Proc. Cambridge Summer School in Logic, 1971), Lecture Notes in Math., vol. 337, Springer-Verlag, Berlin and New York, 1973. MR 0335247 (49:29)
  • [3] G. E. Sacks, On the degrees less than $ 0'$, Ann. of Math. (2) 77 (1963), 211-231. MR 0146078 (26:3604)
  • [4] J. R. Schoenfield and R. I. Soare, The generalized diamond theorem (abstract), Recursive Function Theory Newsletter 19 (1978), no. 219.
  • [5] R. I. Soare, Recursively enumerable sets and degrees, Bull. Amer. Math. Soc. 84 (1978), 1149-1181. MR 508451 (81g:03050)
  • [6] C. E. M. Yates, A minimal pair of r.e. degrees, J. Symbolic Logic 31 (1966), 159-168. MR 0205851 (34:5677)

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