Skip to main content
Log in

Nonstandard methods in combinatorics and theoretical computer science

  • Published:
Studia Logica Aims and scope Submit manuscript

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. S. Albeverio, J. E. Fenstad, R. Høegh-Krohn and T. Lindstrøm, Nonstandard Methods in Stochastic Analysis and Mathematical Physics, Academic Press, New York, 1986.

    Google Scholar 

  2. J. Barwise (ed.), Handbook of Mathematical Logic, North-Holland. Amsterdam. 1977.

    Google Scholar 

  3. J. L. Bell and A. B. Slomson, Model Theory and Ultraproducts, North-Holland, Amsterdam, 1969.

    Google Scholar 

  4. C. C. Chang and H. J. Keisler, Model Theory, North-Holland, Amsterdam, 1973.

    Google Scholar 

  5. D. G. Coyle and M. E. Szabo, Monadic properties of uniformities. Proceedings of the American Mathematical Society 89 (1983), pp. 346–350.

    Google Scholar 

  6. M. Davis, Applied Nonstandard Analysis, Wiley, New York, 1977.

    Google Scholar 

  7. E. J. Farkas and M. E. Szabo, On the plausibility of nonstandard proofs in analysis, Dialectica 38 (1984), pp. 297 310.

    Google Scholar 

  8. C. W. Henson, M. Kaufman andH. J. Keisler, The strength of nonstandard methods in arithmetic, The Journal of Symbolic Logic 49 (1984), 1039–1058.

    Google Scholar 

  9. C. W. Henson and H. J. Keisler, On the strength of nonstandard analysis, The Journal of Symbolic Logic 51 (1986) 377–386.

    Google Scholar 

  10. J. Hirshfeld and M. Machover, Lectures on Nonstandard Analysis, Lecture Notes in Mathematics 94, Springer Verlag, Berlin, 1969.

    Google Scholar 

  11. A. E. Hurd and P. A. Loeb, An Introduction to Nonstandard Real Analysis, Academic Press, Orlando, 1985.

    Google Scholar 

  12. H. J. Keisler, Foundations of Infinitesimal Calculus, Prindie, Weber and Schmidt, Boston, 1977.

    Google Scholar 

  13. D. Laugwitz and C. Shmieden, Eine Erweiterung der Infinitesimalrechnung, Mathematische Zeitschrift 69 (1958), pp. 1–39.

    Google Scholar 

  14. A. H. Lightstone and A. Robinson, Non-Archimedean Fields and Asymptotic Expansions, North-Holland, Amsterdam, 1975.

    Google Scholar 

  15. E. Nelson, Internal set theory, Bulletin of the American Mathematical Society 83 (1977), pp. 1165–1198.

    Google Scholar 

  16. M. M. Richter, Ideale Punkte, Monaden, und Nichtstandard-Methoden, Vieweg, Darmstadt, 1982.

    Google Scholar 

  17. M. M. Richter and M. E. Szabo, Towards a nonstandard analysis of programs, in: A. E. Hurd (ed.), Nonstandard Analysis — Recent Developments, Lecture Notes in Mathematics 983 (1983), Springer-Verlag, pp. 186 203.

  18. M. M. Richter and M. E. Szabo, Nonstandard computation theory, in: J. Demetrovics, G. Katona and A. Salomaa (eds.), Algebra, Combinatorics and Logic in Computer Science, Colloquia Mathematica Societatis János Bolyai 42 (1985), North-Holland, pp. 667–693.

  19. A. Robinson, Nonstandard Analysis, North-Holland, Amsterdam, 1974.

    Google Scholar 

  20. K. Stroyan and J. Bayod, Foundations of Infinitesimal Stochastic Analysis, North-Holland, Amsterdam, 1985.

    Google Scholar 

  21. K. D. Stroyan and W. A. J. Luxemburg, Introduction to the Theory of Infinitesimals, Academic Press, New York, 1976.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

The research of the second author is supported by N.S.E.R.C. Grant A8224 and F.C.A.R. Grant 88-EQ-3491.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Richter, M.M., Szabo, M.E. Nonstandard methods in combinatorics and theoretical computer science. Stud Logica 47, 181–191 (1988). https://doi.org/10.1007/BF00370549

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00370549

Keywords