Bulletin of the American Mathematical Society

Review: Martin Davis, Applied nonstandard analysis, and K. D. Stroyan and W. A. J. Luxemburg, Introduction to the theory of infinitesimals, and H. Jerome Keisler, Foundations of infinitesimal calculus

Andreas Blass

Full-text: Open access

Article information

Bull. Amer. Math. Soc., Volume 84, Number 1 (1978), 34-41.

First available in Project Euclid: 4 July 2007

Permanent link to this document


Blass, Andreas. Review: Martin Davis, Applied nonstandard analysis , and K. D. Stroyan and W. A. J. Luxemburg, Introduction to the theory of infinitesimals , and H. Jerome Keisler, Foundations of infinitesimal calculus. Bull. Amer. Math. Soc. 84 (1978), no. 1, 34--41. https://projecteuclid.org/euclid.bams/1183540371

Export citation


  • 1. A. R. Bernstein and A. Robinson, Solution of an invariant subspace problem of K. T. Smith and P. R. Halmos, Pacific J. Math. 16 (1966), 421-431.
  • 2. A. R. Bernstein and F. Wattenberg, Nonstandard measure theory, in [10], pp. 171-185.
  • 3. D. Brown and A. Robinson, A limit theorem on the cores of large standard exchange economies, Proc. Nat. Acad. Sci. 69 (1972), 1258-1260.
  • 4. P. Howard, Łoś's theorem and the Boolean prime ideal theorem imply the axiom of choice, Proc. Amer. Math. Soc. 49 (1975), 426-428.
  • 5. A. Hurd and P. Loeb (editors), Victoria symposium on nonstandard analysis, Lecture Notes in Math., no. 369, Springer-Verlag, Berlin and New York, 1974.
  • 6. H. J. Keisler, Elementary calculus, Prindle, Weber & Schmidt, Boston, 1976.
  • 7. H. J. Keisler, Hyperfinite model theory (preprint).
  • 8. P. J. Kelemen and A. Robinson, The nonstandard $łambda :\varphi \sp{4}\sb{2}(x):$ model, J. Math. Phys. 13 (1972), 1870-1878.
  • 9. P. Loeb, Conversion from nonstandard to standard measure spaces and applications to probability theory, Trans. Amer. Math. Soc. 211 (1975), 113-122.
  • 10. W. A. J. Luxemburg (editor), Applications of model theory to algebra, analysis, and probability, Holt, Rinehart and Winston, New York, 1969.
  • 11. W. A. J. Luxemburg and A. Robinson (editors), Contributions to nonstandard analysis, North-Holland, Amsterdam, 1972.
  • 12. R. Parikh and M. Parnes, Conditional probabilities and uniform sets, in [5], pp. 180-194.
  • 13. A. Robinson, Nonstandard analysis, Proc. Nederl. Akad. Wetensch. 64 (1961), 432-440.
  • 14. A. Robinson, Non-standard analysis, North-Holland, Amsterdam, 1966.