Finite sets in Quine's new foundations

Journal of Symbolic Logic 34 (4):589-596 (1969)
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Abstract

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).

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1970

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10.2307/2270852

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Citations of this work

Automorphisms of models of set theory and extensions of NFU.Zachiri McKenzie - 2015 - Annals of Pure and Applied Logic 166 (5):601-638.
On the Typed Properties in Quine's “New Foundations”.André Pétry - 1979 - Mathematical Logic Quarterly 25 (7‐12):99-102.

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References found in this work

Logic for Mathematicians.A. Robinson - 1953 - Journal of Symbolic Logic 18 (4):326-327.
Typical Ambiguity.Ernst P. Specker - 1962 - In Ernest Nagel (ed.), Logic, methodology, and philosophy of science. Stanford, Calif.,: Stanford University Press. pp. 116--23.

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