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A quasi-intumonistic set theory

Published online by Cambridge University Press:  12 March 2014

Leslie H. Tharp
Leslie H. Tharp*
Affiliation:
The Rockefeller University, New York, New York 10021
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Extract

It is natural, given the usual iterative description of the universe of sets, to investigate set theories which in some way take account of the unfinished character of the universe. We do not here consider any arguments aimed at justifying one system over another, or at clarifying the basic philosophy. Rather, we look at an obvious candidate which is similar to a system discussed by L. Pozsgay in [1]. Pozsgay sketched the development of the ordinary theorems in such a system and attempted to show it equiconsistent with ZF. In this paper we show that the consistency of the system we call IZF can be proved in the usual ZF set theory.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 36 , Issue 3 , September 1971 , pp. 456 - 460
Copyright
Copyright © Association for Symbolic Logic 1972

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References

[1]Pozsgay, Lawrence, Semi-intuitionistic set theory, Department of Mathematics Preprints, The University of Oklahoma, 1968.1Google Scholar
[2]Kleene, S. C., Introduction to metamathematics, Van Nostrand, Princeton, N.J., 1952.Google Scholar