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Book Review

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Book Information:

Author: Martin Davis
Title: Applied nonstandard analysis
Additional book information: Wiley, New York, London, Sydney, Toronto, 1977, xii + 181 pp., $16.95.

Authors: K. D. Stroyan and W. A. J. Luxemburg
Title: Introduction to the theory of infinitesimals
Additional book information: Academic Press, New York, San Francisco, London, 1976, xiii + 326 pp., $24.50.

Author: H. Jerome Keisler
Title: Foundations of infinitesimal calculus
Additional book information: Prindle, Weber & Schmidt, Boston, 1976, ix + 214 pp.

References [Enhancements On Off] (What's this?)

  • 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. MR 193504
  • 2. A. R. Bernstein and F. Wattenberg, Nonstandard measure theory, in [10], pp. 171-185. MR 247018
  • 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. MR 384548
  • 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. MR 472459
  • 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. MR 390154
  • 10. W. A. J. Luxemburg (editor), Applications of model theory to algebra, analysis, and probability, Holt, Rinehart and Winston, New York, 1969. MR 234829
  • 11. W. A. J. Luxemburg and A. Robinson (editors), Contributions to nonstandard analysis, North-Holland, Amsterdam, 1972. MR 476972
  • 12. R. Parikh and M. Parnes, Conditional probabilities and uniform sets, in [5], pp. 180-194. MR 482898
  • 13. A. Robinson, Nonstandard analysis, Proc. Nederl. Akad. Wetensch. 64 (1961), 432-440. MR 142464
  • 14. A. Robinson, Non-standard analysis, North-Holland, Amsterdam, 1966. MR 205854

Review Information:

Reviewer: Andreas Blass
Journal: Bull. Amer. Math. Soc. 84 (1978), 34-41
DOI: https://doi.org/10.1090/S0002-9904-1978-14401-2
American Mathematical Society