Система NFI, равнонепротиворечивая с системой куайна NF.
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03.10.2002
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Аннотация
We suggest an intuitionistic variant of the famous W. Quine’s NF which we call NFI and which is equiconsistent with NF.
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Хаханян В. Система NFI, равнонепротиворечивая с системой куайна NF. // Логические исследования / Logical Investigations. 2002. Т. 9. C. 245-250.
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Литература
Гришин В.Н., Драгалин А .Г Аксиоматическая теория множеств // Математическая энциклопедия. Т. 1. 1977. С. 104-109.
Драгалин А.Г. Математический интуиционизм. Е1ведение в теорию доказательств. М.: Наука, 1979. С. 46
Boffa М. The consistency problem for NF, The Journal of Symbolic Logic. Vol. 42, No. 2. June 1977, P. 215-220.
Boffa M. The point on Quine’s NF (with a bibliography) // Theoria IV, (2), 3-15 (1984).
Friedman H. The consistency of classical set theory relative to a set theory with intuitionistic logic II The Journal of Symbolic Logic. Vol. 38, No. 2. 1973, P.315-319.
Posser J.B. Logic for mathematicians // Chelsea Publishing Co., New York, 1978, XYI + 574 p. Appendix A
Pow ell W.R. Extending Godel s negative interpretation to ZF // The Journal of Symbolic Logic. Vol. 40, No. 2. 1975, P.221-229.
Quine W. New Foundations for mathematical logic // American Mathem. Monthly. Vol. 44. P. 70-80.
Specker E. The axiom of choice in Quine’s New Foundations for mathematical logic // Proceedings of National Academy of Science of the USA. Vol. 39, 1953, P. 972-975.
Specker E. Typical ambiguity Logic, methodology and philosophy of science // Proceedings of the 1960 International Congress, Stanford, 1962, P.116-124.
Драгалин А.Г. Математический интуиционизм. Е1ведение в теорию доказательств. М.: Наука, 1979. С. 46
Boffa М. The consistency problem for NF, The Journal of Symbolic Logic. Vol. 42, No. 2. June 1977, P. 215-220.
Boffa M. The point on Quine’s NF (with a bibliography) // Theoria IV, (2), 3-15 (1984).
Friedman H. The consistency of classical set theory relative to a set theory with intuitionistic logic II The Journal of Symbolic Logic. Vol. 38, No. 2. 1973, P.315-319.
Posser J.B. Logic for mathematicians // Chelsea Publishing Co., New York, 1978, XYI + 574 p. Appendix A
Pow ell W.R. Extending Godel s negative interpretation to ZF // The Journal of Symbolic Logic. Vol. 40, No. 2. 1975, P.221-229.
Quine W. New Foundations for mathematical logic // American Mathem. Monthly. Vol. 44. P. 70-80.
Specker E. The axiom of choice in Quine’s New Foundations for mathematical logic // Proceedings of National Academy of Science of the USA. Vol. 39, 1953, P. 972-975.
Specker E. Typical ambiguity Logic, methodology and philosophy of science // Proceedings of the 1960 International Congress, Stanford, 1962, P.116-124.