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Book Review

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Book Information:

Authors: A. H. Lightstone and A. Robinson
Title: Non-archimedean fields and asymptotic expansions
Additional book information: North-Holland Mathematical Library, vol. 13, North-Holland/American Elsevier, Amsterdam and New York, 1975, 204 + x pp., $24.95.

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

  • 1. D. Laugwitz, Eine nichtarchimedische Erweiterung angeordneter Körper, Math. Nachr. 37 (1968), 225-236. MR 39 #4125. MR 242798
  • 2. T. Levi-Civita, Sugli infiniti ed infinitesimali actuali quali elementi analytici, Opere Matematiche, Vol. 1. 1893-1900, Bologna, 1954, pp. 1-39. MR 16, 1. MR 62680
  • 3. W. A. J. Luxemburg, Non-standard analysis. Lectures on A. Robinson's theory of infinitesimals and infinitely large numbers, Calif. Inst, of Technology, Pasadena, Calif., 1962 (mimeographed notes). MR 491162
  • 4. A. Ostrowski, Untersuchungen zur arithmetischen Theorie der Körper, Math. Z. 39 (1934), 269-404.
  • 5. J. Popken, Asymptotic expansions from an algebraic standpoint, Nederl. Akad. Wetensch. Proc. Ser. A 56 = Indag. Math. 15 (1953), 131-143. MR 15, 27. MR 56114
  • 6. Abraham Robinson, Non-standard analysis, North-Holland, Amsterdam, 1966. MR 34 #5680. MR 205854
  • 7. Abraham Robinson, Elementary embeddings of fields of power series, J. Number Theory 2 (1970), 237-247. MR 41 #3451. MR 258805
  • 8. Abraham Robinson, On the real closure of a Hardy field, Theory of Sets and Topology (Hausdorff Memorial Volume, G. Asser et al., editors), VEB Deutsch. Verlag Wissensch., Berlin, 1972, pp. 427-433. MR 49 #4980. MR 340225
  • 9. Abraham Robinson, Function theory on some nonarchimedean fields, Papers in the Foundations of Mathematics, Amer. Math. Monthly 80 (1973), 87-109. MR 48 #8464. MR 330126

Review Information:

Reviewer: Peter A. Loeb
Journal: Bull. Amer. Math. Soc. 83 (1977), 231-235
DOI: https://doi.org/10.1090/S0002-9904-1977-14277-8
American Mathematical Society