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On the extension principle in internal set theory

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References

  1. E. Nelson, “Internal set theory: a new approach to nonstandard analysis,” Bull. Amer. Math. Soc.,83, No. 6, 1165–1198 (1977).

    Google Scholar 

  2. E. Nelson, “The syntax of nonstandard analysis,” Ann. Pure Appl. Logic,38, No. 2, 123–134 (1988).

    Google Scholar 

  3. V. G. Kanoveį, “Set theoretic incompleteness of Edward Nelson's internal set theory,” in: Abstracts. Proc. Tenth All-Union Conference on Logic [in Russian], Alma-Ata, 1990, p. 75.

  4. V. G. Kanoveį, “Bounded sets in internal set theory,” Abstracts. Proc. Tenth All-Union Seminar on Nonstandard Analysis [in Russian], Saratov, 1990, pp. 15–23.

  5. I. van den Berg, Nonstandard Asymptotic Analysis (Lecture Notes in Math.,1249), Springer, Berlin (1987).

    Google Scholar 

  6. F. Diener and K. D. Stroyan, “Syntactical methods in infinitesimal analysis,” in: Nonstandard Analysis and Its Applications (London Math. Soc. Stud. Texts,10), Cambridge Univ. Press, Cambridge, 1988, pp. 258–281.

    Google Scholar 

  7. O. Loos, “A non-standard approach to the Lebesgue integral,” in: Mathematiques Finitaires et Analyse non Standard, Paris, 1985, pp. 27–35.

  8. R. Lutz and M. Gose, Nonstandard Analysis: a Practical Guide with Applications (Lecture Notes in Math.,881), Springer, Berlin (1981).

    Google Scholar 

  9. K. Hrbaček, “Axiomatic foundations for nonstandard analysis,” Fund. Math.,98, No. 1, 1–19 (1978).

    Google Scholar 

  10. T. Kawai, “Nonstandard analysis by axiomatic methods,” in: Southeast Asia Conference on Logic Singapore, 1981 (Stud. in Logic Found. Math.,111), North Holland, Amsterdam, 1983, pp. 55–76.

    Google Scholar 

  11. C. W. Henson and H. G. Keisler, “The strength of nonstandard analysis,” J. Symbolic Logic,51, No. 2, 377–386 (1986).

    Google Scholar 

  12. A. G. Kusraev and S. S. Kutateladze, Nonstandard Methods in Analysis [in Russian], Nauka, Novosibirsk (1990).

    Google Scholar 

  13. V. A. Uspenskiį, What is Nonstandard Analysis? [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  14. T. Lindstrøm, “An invitation to nonstandard analysis,” in: Nonstandard Analysis and Its Applications (London Math. Soc. Stud. Texts,10), Cambridge Univ. Press, Cambridge, 1988, pp. 1–105.

    Google Scholar 

  15. T. Jech, Set Theory and the Method of Forcing [Russian translation], Mir, Moscow (1973).

    Google Scholar 

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Authors
  1. V. G. Kanoveį
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Additional information

Moscow. Translated fromSibirskiį Matematicheskiį Zhurnal, Vol. 33, No. 6, pp. 66–78, November–December, 1992.

Translated by K. M. Umbetova

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Kanoveį, V.G. On the extension principle in internal set theory. Sib Math J 33, 999–1010 (1992). https://doi.org/10.1007/BF00971023

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  • DOI: https://doi.org/10.1007/BF00971023

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