Notre Dame Journal of Formal Logic

A Strong Model of Paraconsistent Logic

Olivier Esser
Source: Notre Dame J. Formal Logic Volume 44, Number 3 (2003), 149-156.

Abstract

The purpose of this paper is mainly to give a model of paraconsistent logic satisfying the "Frege comprehension scheme" in which we can develop standard set theory (and even much more as we shall see). This is the continuation of the work of Hinnion and Libert.

First Page: Show Hide
Primary Subjects: 03B50, 03B53, 03E70
Secondary Subjects: 54A99
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1091030853
Digital Object Identifier: doi:10.1305/ndjfl/1091030853
Mathematical Reviews number (MathSciNet): MR2130787
Zentralblatt MATH identifier: 02187145

References

[1] Avron, A., "Natural $3$"-valued logics---characterization and proof theory, The Journal of Symbolic Logic, vol. 56 (1991), pp. 276--94.
Mathematical Reviews (MathSciNet): MR93b:03032
Zentralblatt MATH: 0745.03017
[2] Batens, D., and K. De Clercq, "A rich paraconsistent extension of full positive logic", available at http://logica.rug.ac.be/centrum/writings/.
[3] Esser, O., "Mildly ineffable cardinals and hyperuniverses", forthcoming in Reports on Mathematical Logic.
Mathematical Reviews (MathSciNet): MR2047926
[4] Esser, O., "An interpretation of the Zermelo-Fraenkel set theory and the Kelley-Morse set theory in a positive theory", Mathematical Logic Quarterly, vol. 43 (1997), pp. 369--77.
Mathematical Reviews (MathSciNet): MR98i:03068
Zentralblatt MATH: 0880.03030
[5] Esser, O., "On the consistency of a positive theory", Mathematical Logic Quarterly, vol. 45 (1999), pp. 105--16.
Mathematical Reviews (MathSciNet): MR2000e:03145
Zentralblatt MATH: 0924.03102
[6] Esser, O., "On the axiom of extensionality in the positive set theory", Mathematical Logic Quarterly, vol. 49 (2003), pp. 97--100.
Mathematical Reviews (MathSciNet): MR2004b:03099
Zentralblatt MATH: 1015.03054
Digital Object Identifier: doi:10.1002/malq.200310009
[7] Forti, M., and R. Hinnion, "The consistency problem for positive comprehension principles", The Journal of Symbolic Logic, vol. 54 (1989), pp. 1401--18.
Mathematical Reviews (MathSciNet): MR91d:03020
Zentralblatt MATH: 0702.03026
[8] Forti, M., and F. Honsell, "A general construction of hyperuniverses", Theoretical Computer Science, vol. 156 (1996), pp. 203--15.
Mathematical Reviews (MathSciNet): MR97d:03072
Zentralblatt MATH: 0871.68131
Digital Object Identifier: doi:10.1016/0304-3975(95)00087-9
[9] Gilmore, P. C., "The consistency of partial set theory without extensionality", pp. 147--53 in Axiomatic Set Theory (Proceedings of Symposia in Pure Mathematics, vol. 13, part 2, University of California, Los Angeles, 1967), American Mathematical Society, Providence, 1974.
Mathematical Reviews (MathSciNet): MR50:12721
Zentralblatt MATH: 0309.02065
[10] Hinnion, R., "Extensional quotients of structures and applications to the study of the axiom of extensionality", Bulletin de la Société Mathématique de Belgique. Série B, vol. 33 (1981), pp. 173--206.
Mathematical Reviews (MathSciNet): MR84c:03089
Zentralblatt MATH: 0484.03029
[11] Hinnion, R., "Naï"ve set theory with extensionality in partial logic and in paradoxical logic, Notre Dame Journal of Formal Logic, vol. 35 (1994), pp. 15--40.
Mathematical Reviews (MathSciNet): MR95c:03063
Zentralblatt MATH: 0801.03019
Digital Object Identifier: doi:10.1305/ndjfl/1040609292
Project Euclid: euclid.ndjfl/1040609292
[12] Libert, T., "ZF and the axiom of choice in some paraconsistent set theories", forthcoming.
Mathematical Reviews (MathSciNet): MR2049085
[13] Malitz, R. J., Set Theory in Which the Axiom of Foundation Fails, Ph.D. thesis, University of California, 1976. Available from University Microfilms International, Ann Arbor, MI 48106.

2012 © University of Notre Dame

Notre Dame Journal of Formal Logic

Notre Dame Journal of Formal Logic

Turn MathJax Off
What is MathJax?