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A positive set theory with equality revisited

Published online by Cambridge University Press:  01 February 2008

GIACOMO LENZI*
Affiliation:
c/o Department of Mathematics, University of Pisa, Largo Pontecorvo 5, Pisa, Italy Email: lenzi@mail.dm.unipi.it

Abstract

This paper is the journal version of Lenzi (2006). We consider the positive set theory with equality described these and propose a candidate model.

Type
Paper
Copyright
Copyright © Cambridge University Press2008

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References

Brady, R. (1971) The consistency of the axioms of abstraction and extensionality in a three-valued logic. Notre Dame Journal of Formal Logic 12 4447453.CrossRefGoogle Scholar
Gilmore, P. (1974) The consistency of partial set theory without extensionality. In: Proceedings of Symposia in Pure Mathematics 13 2147153.CrossRefGoogle Scholar
Hinnion, R. (1987) Le paradoxe de Russell dans les versions positives de la théorie naïve des ensembles. C. R. Acad. Sci. Paris, Série I 304 12307310.Google Scholar
Hinnion, R. (1994) Naïve set theory with extensionality in partial logic and paradoxical logic. Notre Dame Journal of Formal Logic 35 11540.CrossRefGoogle Scholar
Lenzi, G. (1992) Weydert's SF3 has no recursive term model. Bull. Soc. Math. Belg. 44 3311327.Google Scholar
Lenzi, G. (1999) A nontrivial model of Weydert's SF3 minus the Leibniz rules. Bull. Soc. Math. Belg. 6 7790.Google Scholar
Lenzi, G. (2006) About a positive set theory with equality. Contributed paper to the conference LMCS 2006 (a conference in memory of Sauro Tulipani), Camerino.Google Scholar
Skolem, T. (1963) Studies on the axiom of comprehension. Notre Dame J. Formal Logic 3 4162170.Google Scholar
Weydert, E. (1989) How to approximate the naive comprehension scheme inside of classical logic, Ph.D. Thesis, University of Bonn.Google Scholar