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Rice Theorems For D.R.E. Sets

Published online by Cambridge University Press:  20 November 2018

Louise Hay
Louise Hay*
Affiliation:
University of Illinois at Chicago Circle, Chicago, Illinois
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Two of the basic theorems in the classification of index sets of classes of recursively enumerable (r.e.) sets are the following:

(i) The index set of a class C of r.e. sets is recursive if and only if C is empty or contains all r.e. sets; and

(ii) the index set of a class C or r.e. sets is recursively enumerable if and only if C is empty or consists of all r.e. sets which extend some element of a canonically enumerable class of finite sets.

The first theorem is due to Rice [7, p. 364, Corollary B]. The second was conjectured by Rice [7, p. 361] and proved independently by McNaughton, Shapiro, and Myhill [6].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 2 , 01 April 1975 , pp. 352 - 365
Copyright
Copyright © Canadian Mathematical Society 1975

References

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6. Myhill, J., A fixed point theorem in recursion theory, Abstract, J. Symbolic Logic 20 (1955), p. 205.Google Scholar
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