Book Review

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MathSciNet review: 1567016

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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.

**1.**Allen R. Bernstein and Abraham 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.**Allen R. Bernstein and Frank Wattenberg,*Nonstandard measure theory*, Applications of Model Theory to Algebra, Analysis, and Probability (Internat. Sympos., Pasadena, Calif., 1967) Holt, Rinehart and Winston, New York, 1969, pp. 171–185. MR**0247018****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.**Paul E. Howard,*Łoś’ theorem and the Boolean prime ideal theorem imply the axiom of choice*, Proc. Amer. Math. Soc.**49**(1975), 426–428. MR**384548**, https://doi.org/10.1090/S0002-9939-1975-0384548-X**5.**Albert Hurd and Peter Loeb (eds.),*Victoria Symposium on Nonstandard Analysis*, Lecture Notes in Mathematics, Vol. 369, Springer-Verlag, Berlin-New York, 1974. Held at the University of Victoria, Victoria, B. C., 8–11 May 1972. MR**0472459****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.**Peter A. Loeb,*Conversion from nonstandard to standard measure spaces and applications in probability theory*, Trans. Amer. Math. Soc.**211**(1975), 113–122. MR**390154**, https://doi.org/10.1090/S0002-9947-1975-0390154-8**10.***Applications of model theory to algebra, analysis, and probability.*, Edited by W. A. J. Luxemburg, Holt, Rinehart and Winston, New York-Montreal, Que.-London, 1969. MR**0234829****11.***Contributions to non-standard analysis*, North-Holland Publishing Co., Amsterdam-London, 1972. A collection of papers based on lectures given at the Symposium on Non-standard Analysis, Oberwolfach, July 19–July 25, 1970; Edited by W. A. J. Luxemburg and A. Robinson; Studies in Logic and the Foundations of Mathematics, Vol. 69. MR**0476972****12.**Rohit Parikh and Milton Parnes,*Conditional probabilities and uniform sets*, Victoria Symposium on Nonstandard Analysis (Univ. Victoria, Victoria, B.C., 1972) Springer, Berlin, 1974, pp. 180–194. Lecture Notes in Math., Vol. 369. MR**0482898****13.**Abraham Robinson,*Non-standard analysis*, Nederl. Akad. Wetensch. Proc. Ser. A 64 = Indag. Math.**23**(1961), 432–440. MR**0142464****14.**Abraham Robinson,*Non-standard analysis*, North-Holland Publishing Co., Amsterdam, 1966. MR**0205854**

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