Bulletin of the American Mathematical Society

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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.

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

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.

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, DOI 10.1090/S0002-9939-1975-0384548-X

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.

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, DOI 10.1090/S0002-9947-1975-0390154-8

W. A. J. Luxemburg (ed.), Applications of model theory to algebra, analysis, and probability. , Holt, Rinehart and Winston, New York-Montreal, Que.-London, 1969. MR 0234829

Contributions to non-standard analysis, Studies in Logic and the Foundations of Mathematics, Vol. 69, 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. MR 0476972

Rohit Parikh and Milton Parnes, Conditional probabilities and uniform sets, Victoria Symposium on Nonstandard Analysis (Univ. Victoria, Victoria, B.C., 1972) Lecture Notes in Math., Vol. 369, Springer, Berlin, 1974, pp. 180–194. MR 0482898

Abraham Robinson, Non-standard analysis, Nederl. Akad. Wetensch. Proc. Ser. A 64 = Indag. Math. 23 (1961), 432–440. MR 0142464

Abraham Robinson, Non-standard analysis, North-Holland Publishing Co., Amsterdam, 1966. MR 0205854

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 0193504

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