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A generalisation of productive set

Published online by Cambridge University Press:  12 March 2014

R. Mitchell
R. Mitchell*
Affiliation:
Bristol College of Science and Technology
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Extract

The purpose of the present paper is to introduce a generalisation of the concept of productive set introduced by Post (2) and studied by Dekker (3) and others. Throughout the paper we shall use small Latin letters to denote both non-negative integers (referred to as numbers) and functions (both partial and total) from numbers to numbers. Sets of numbers will be denoted by small Greek letters and classes of such sets by capital Latin letters. ωη is the range of the ηth partial recursive function.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 31 , Issue 3 , 02 September 1966 , pp. 455 - 459
Copyright
Copyright © Association for Symbolic Logic 1996

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References

[1]Mitchell, R., Some properties of non-recursive sets, Ph. D. Thesis, University of Newcastle upon Tyne, May 1962.Google Scholar
[2]Post, E. L., Recursively enumerable sets of positive integers and their decision problems, Bull. Amer. Math. Soc., vol. 50 (1944), pp. 284–316.CrossRefGoogle Scholar
[3]Dekker, J., Productive sets, Trans. Amer. Math. Soc., vol. 78 (1955), pp. 129–149.CrossRefGoogle Scholar
[4]Myhill, J., Creative sets, Zeit. für Math. Log. und Grund. der Math., vol. 1 (1955), pp. 97–108.CrossRefGoogle Scholar