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Compact and majorizable functionals of finite type

Published online by Cambridge University Press:  12 March 2014

Marc Bezem
Marc Bezem*
Affiliation:
Centre for Mathematics and Computer Science, P.O. Box 4079, 1009 Ab Amsterdam, The Netherlands
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Extract

The main result of this paper will be that various notions of majorizability and compactness coincide in the full typestructure over the natural numbers. Moreover we shall show that the extensional typestructure of strongly majorizable functionals can be obtained by applying Zucker's construction ( )E to any of these coinciding intensional typestructures. A different result is proved in the typestructure of effective operations, where not every majorizable functional is compact. Finally we shall introduce the concept of relative compactness in the full typestructure and prove that there are just two degrees of compactness.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 54 , Issue 1 , March 1989 , pp. 271 - 280
Copyright
Copyright © Association for Symbolic Logic 1989

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References

REFERENCES

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