Skip to main content
SpringerLink
Log in
Book cover

International Conference on Computer Logic

COLOG 1988: COLOG-88 pp 146–197Cite as

Mathematics of infinity

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 417))

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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. P. Aczel, Non-Well-Founded Sets, CSLI Lecture Notes, Number 14, Stanford University, 1988.

    Google Scholar 

  3. A. Robinson, Non-standard Analysis, North-Holland Publishing Company, Amsterdam, 1966.

    Google Scholar 

  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 

  5. E. Bishop, Foundations of Constructive Analysis, McGraw-Hill Book Company, New York, 1967.

    Google Scholar 

  6. 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 

  7. 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 

  8. P. Martin-Löf, Intuitionistic Type Theory, Bibliopolis, Napoli, 1984.

    Google Scholar 

  9. 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 

  10. A. S. Troelstra, op. cit.,, p. 154.

    Google Scholar 

  11. 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 

  12. P. Martin-Löf, op. cit., pp. 69–70.

    Google Scholar 

  13. A. Robinson, op. cit., pp. 36–37.

    Google Scholar 

  14. For a nonstandard version of the Cantor space in classical nonstandard analysis, see S. Albeverio et al., op. cit., p. 65.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Stockholm, Box 6701, 113 85, Stockholm, Sweden

    Per Martin-Löf

Authors
  1. Per Martin-Löf
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Per Martin-Löf Grigori Mints

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Martin-Löf, P. (1990). Mathematics of infinity. In: Martin-Löf, P., Mints, G. (eds) COLOG-88. COLOG 1988. Lecture Notes in Computer Science, vol 417. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52335-9_54

Download citation

  • DOI: https://doi.org/10.1007/3-540-52335-9_54

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52335-2

  • Online ISBN: 978-3-540-46963-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation