Mathematics of infinity

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


Nonstandard Analysis Transfer Principle Choice Sequence Propositional Function Standard Sense 
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  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
  2. 2.
    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
  4. 4.
    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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    E. Bishop, Foundations of Constructive Analysis, McGraw-Hill Book Company, New York, 1967.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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    A. Robinson, op. cit., pp. 36–37.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 Berlin Heidelberg 1990

Authors and Affiliations

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

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