COLOG-88 pp 146-197 | Cite as

Mathematics of infinity

  • Per Martin-Löf
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 417)

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References

  1. 1.
    Introduced by J. Wallis, De Sectionibus Conicis, Nova, Methodo Expositis, Tractatus, Oxford, 1655, in the laconic parenthesis (esto enim ∞ nota numeri infiniti;), apparently without worrying about its meaningfulness.Google Scholar
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    P. Aczel, Non-Well-Founded Sets, CSLI Lecture Notes, Number 14, Stanford University, 1988.Google Scholar
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    A. Robinson, Non-standard Analysis, North-Holland Publishing Company, Amsterdam, 1966.Google Scholar
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    C. Schmieden and D. Laugwitz, Eine Erweiterung der Infinitesimalrechnung, Mathematische Zeitschrift, Vol. 69, 1958, pp. 1–39. See also the book by D. Laugwitz, Infinitesimalkalkül, Eine elementare Einführung in die Nichtstandard-Analysis, Bibliographisches Institut, Mannheim, 1978, and the further references given there.Google Scholar
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    L. E. J. Brouwer, Begründung der Mengenlehre unabhängig vom logischen Satz vom ausgeschlossenen Dritten. Erster Teil: Allgemeine Mengenlehre, Verhandelingen der Koninklijke Akademie van Wetenschappen te Amsterdam, Sect. 1, Vol. 12, No. 5, 1981, pp. 3–43.Google Scholar
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    D. Scott, Domains for denotational semantics, Lecture Notes in Computer Science, Vol. 140, Automata, Languages and Programming, Edited by M. Nielsen and E. M. Schmidt, Springer-Verlag, Berlin, 1982, pp. 577–613, and P. Aczel, op. cit.Google Scholar
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    P. Martin-Löf, Intuitionistic Type Theory, Bibliopolis, Napoli, 1984.Google Scholar
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    A. S. Troelstra, Choice Sequences, A Chapter of Intuitionistic Mathematics, Clarendon Press, Oxford, 1977. See particularly Appendix C, pp. 152–160, and the references to earlier works given there.Google Scholar
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    A. S. Troelstra, op. cit.,, p. 154.Google Scholar
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    S. Albeverio, J. E. Fenstad, R. Hoegh-Krohn, and T. Lindstrøm, Nonstandard Methods in Stochastic Analysis and Mathematical Physics, Academic Press, New York, 1986, p. 46.Google Scholar
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    P. Martin-Löf, op. cit., pp. 69–70.Google Scholar
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    For a nonstandard version of the Cantor space in classical nonstandard analysis, see S. Albeverio et al., op. cit., p. 65.Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Per Martin-Löf
    • 1
  1. 1.Department of MathematicsUniversity of StockholmStockholmSweden

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