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Combinator realizability of a constructive Morse set theory

Published online by Cambridge University Press:  12 March 2014

John Staples
John Staples*
Affiliation:
Australian National University, Canberra, Act 2600, Australia
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Extract

A constructive version of Morse set theory is given, based on Heyting's predicate calculus and with countable rather than full choice. An elaboration of the method of [5] is used to show that the theory is combinator-realizable in the sense defined there. The proof depends on the assumption of the syntactic consistency of the theory.

The method is introduced by first treating a subtheory without countable choice of foundation.

It is intended that the work can be read either classically or constructively, though whether the word constructive is correctly used as a description of either the theory or the metatheory is of course a matter of opinion.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 39 , Issue 2 , June 1974 , pp. 226 - 234
Copyright
Copyright © Association for Symbolic Logic 1974

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References

REFERENCES

[1] Barendregt, Henk, Combinatory logic and the axiom of choice, Indagationes Mathematicae, vol. 35 (1973), pp. 205–221.Google Scholar
[2] Friedman, H., Some applications of Kleene's methods for intuitionistic systems, Cambridge Summer School in Mathematical Logic (Mathias, A. R. D. and Rogers, H., Editors, Springer, 1973, pp. 113–170.Google Scholar
[3] Kelley, J. L., General topology, van Nostrand, New York, 1955.Google Scholar
[4] Myhill, John, Some properties of intuitionistic Zermelo-Freankel set theory, Cambridge Summer School in Mathematical Logic (Mathias, A. R. D. and Rogers, H., Editor), Springer, Berlin, 1973, pp. 206–231.Google Scholar
[5] Staples, John, Combinator realizability of constructive finite type analysis, Cambridge Summer School in Mathematical Logic (Mathias, A. R. D. and Rogers, H., Editors), Springer, Berlin, 1973, pp. 253–273.Google Scholar