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Effective operations in a general setting

Published online by Cambridge University Press:  12 March 2014

A. H. Lachlan
A. H. Lachlan*
Affiliation:
The University of Newcastle upon Tyne
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Extract

There are essentially two ‘positive’ results concerning the extension of effective operations to partial recursive functionals. The first proved by Myhill and Shepherdson in [9] states that any effective operation whose domain is the set of all partial recursive (p.r.) functions is potentially p.r. The second proved originally by Kreisel, Lacombe, and Shoenfield in [5] states: Let F be an effective operation mapping a set of recursive functions into the natural numbers; if has a recursively dense base, then F is potentially p.r. The main objective of this paper is to present these two theorems in a general setting.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 29 , Issue 4 , December 1964 , pp. 163 - 178
Copyright
Copyright © Association for Symbolic Logic 1964

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References

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