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Mathematical Logic and Applications pp 203–220Cite as

Infinitesimal calculus interpreted in infinitary logic

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1388))

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References

  1. Martin Davis, Applied nonstandard analysis, Wiley (1976).

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  2. Solomon Feferman, Lectures on proof theory, LNM 70 (1968), Springer-Verlag, 1–108.

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  3. Ward Henson and Jerome Keisler, On the strength of nonstandard analysis, JSL 51 (1986), 377–386.

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  4. Yuzuru Kakuda, Theory of infinitesimals without nonstandard models, Kobe J. Math. 2(1985),187–213.

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  5. Toru Kawai, Nonstandard analysis by axiomatic method, Southeast Asian Conference on Logic, Elsevier (1983), 55–76.

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  6. Nobuyoshi Motohashi, Developing nonstandard analysis in a text of proof theory (in Japanese), Proceedings of RIMS 436 (1980), 135–149.

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  7. Edward Nelson, The syntax of nonstandard analysis, mimeographed notes.

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  8. Abraham Robinson, Nonstandard analysis, 2nd ed., American Elsevier, New York (1974).

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  9. Masahiko Saito, “What is nonstandard analysis?” (in Japanese), Sugaku 38 (1986), 133–149.

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Author information

Authors and Affiliations

  1. Faculty of Science, Kyoto Sangyo University, Kita-ku, 603, Kyoto, Japan

    Mariko Yasugi

Authors
  1. Mariko Yasugi
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Juichi Shinoda Tosiyuki Tugué Theodore A. Slaman

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Dedicated to Professor Shôji Maehara on his sixtieth birthday

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© 1989 Springer-Verlag

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Yasugi, M. (1989). Infinitesimal calculus interpreted in infinitary logic. In: Shinoda, J., Tugué, T., Slaman, T.A. (eds) Mathematical Logic and Applications. Lecture Notes in Mathematics, vol 1388. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083672

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  • DOI: https://doi.org/10.1007/BFb0083672

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51527-2

  • Online ISBN: 978-3-540-48220-8

  • eBook Packages: Springer Book Archive

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