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Effective operations in a general setting

Published online by Cambridge University Press:  12 March 2014

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

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
Copyright
Copyright © Association for Symbolic Logic 1964

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References

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