Preview
Unable to display preview. Download preview PDF.
References
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.
P. Aczel, Non-Well-Founded Sets, CSLI Lecture Notes, Number 14, Stanford University, 1988.
A. Robinson, Non-standard Analysis, North-Holland Publishing Company, Amsterdam, 1966.
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.
E. Bishop, Foundations of Constructive Analysis, McGraw-Hill Book Company, New York, 1967.
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.
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.
P. Martin-Löf, Intuitionistic Type Theory, Bibliopolis, Napoli, 1984.
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.
A. S. Troelstra, op. cit.,, p. 154.
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.
P. Martin-Löf, op. cit., pp. 69–70.
A. Robinson, op. cit., pp. 36–37.
For a nonstandard version of the Cantor space in classical nonstandard analysis, see S. Albeverio et al., op. cit., p. 65.
Author information
Authors and Affiliations
Editor information
Rights 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