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Finite sets in Quine's new foundations1

Published online by Cambridge University Press:  12 March 2014

C. Ward Henson
C. Ward Henson*
Affiliation:
Duke University
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Extract

In this paper we consider some axiomatic systems of set theory related to the system NF (New Foundations) of Quine. In particular we discuss the possible relations of cardinality between a finite set x and its subset class SC(x) = {y | y ∩ x} and also between x and its unit set class USC(x) = {{y} | y ε x}. Specker [5] has shown that in NF the cardinal of a finite set x can never be the same as the cardinal of SC(x).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 34 , Issue 4 , February 1970 , pp. 589 - 596
Copyright
Copyright © Association for Symbolic Logic 1970

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Footnotes

1

An earlier version of some of the results in this paper appeared in the author's Ph.D. thesis which was presented to the Massachusetts Institute of Technology. The author is indebted to Hilary Putnam for his helpful advice and encouragement during work on this thesis.

References

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