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On a Class of Complete Simple Sets

Published online by Cambridge University Press:  20 November 2018

T. G. McLaughlin
T. G. McLaughlin*
Affiliation:
University of Illinois
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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 1 , February 1965 , pp. 33 - 37
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Post, E. L., Recursively enumerable sets of positive integers and their decision problems, Bull. Amer. Math. Soc., 50 (1944), 284-316.Google Scholar
2. Sacks, G. E., A simple set which is not effectively simple, Proc. Amer. Math. Soc., 15(1964), 51-55.Google Scholar
3. Schoenfield, J. R., Quasicreative sets, Proc. Amer. Math. Soc., 8 (1957), 964-967.Google Scholar