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A partial model of NF with E

Published online by Cambridge University Press:  12 March 2014

N. Prati
N. Prati*
Affiliation:
Dipartimento di Finanze, Facolta di Economia, Università Degli Studi di Udine, Via Tomadini 30, 33100 Udine, Italy
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Abstract

Partial models of the theory New Foundations (NF) introduced by Quine have already appeared in the literature, but in every model the membership set of NF is missing. On the other hand, Jensen showed that “NF + Urelements” is consistent with respect to ZF and, in the model built there, the membership set of the theory exists, Here we build a partial model of NF from the one of Jensen in which the membership set exists.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 59 , Issue 4 , December 1994 , pp. 1245 - 1253
Copyright
Copyright © Association for Symbolic Logic 1994

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References

REFERENCES

[Be]Benes, V. E., A partial model of Quine's “New Foundations”, this Journal, vol. 19 (1954), pp. 197–200.Google Scholar
[B1]Boffa, M., The consistency problem for NF, this Journal, vol. 42 (1977), pp. 215–220.Google Scholar
[B2]Boffa, M., The point on Quine's NF, Teoria, vol. IV (1984), pp. 3–13.Google Scholar
[B3]Boffa, M., La théorie de type et NF, Bulletin de la Société Mathématique de Belgique, Serie A, vol. XXXIII (1981), pp. 21–31.Google Scholar
[B4]Boffa, M., The consistency of ZF + NF3, Mathematische Forschungsinstitut Oberwolfach, Tagungsbericht, no. 9 (1987).Google Scholar
[B-C]Boffa, M. and Casalegno, P., The consistency of some 4-stratified subsystem of NF including NF3, this Journal, vol. 50 (1985). pp. 407–411.Google Scholar
[G]Grishin, V. N., The equivalence of Quine's NF system to a fragment of it, Automatic Documentation and Mathematical Linguistic (1972), pp. 15–19; English translation of a paper in Nauchno-Tekhnicheskaya Informatsiya, Series 2, vol. 6 (1972), no. 1, pp. 22–24.Google Scholar
[H]Hailperin, T., A set of axioms for logic, this Journal, vol. 9 (1944), pp. 1–19.Google Scholar
[J]Jensen, R. B., On the consistency of a slight (?) modification of Quine's New Foundations, Synthese, vol. 19 (1968/1969), pp. 250–263.CrossRefGoogle Scholar
[L]Lake, J., Some topics on set theory, Ph.D. Thesis, Bedford College, London University, London, 1974.Google Scholar
[P]Prati, N., A partial model of NF with ZF, Mathematical Logic Quarterly, vol. 39 (1993), pp. 274–278.CrossRefGoogle Scholar
[Q]Quine, W. V., New foundations for mathematical logic, American Mathematical Monthly, vol. 44 (1937), pp. 70–80.CrossRefGoogle Scholar
[S]Specker, E., Typical ambiguity, Logic, Methodology and Philosophy of Science (Nagel, E.et al., editors), Proceedings of the 1960 International Congress, Stanford University Press, Stanford, California, 1962, pp. 116–124.Google Scholar