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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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The real field with convergent generalized power series
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by Lou van den Dries and Patrick Speissegger PDF
Trans. Amer. Math. Soc. 350 (1998), 4377-4421 Request permission

Abstract:

We construct a model complete and o-minimal expansion of the field of real numbers in which each real function given on $[0,1]$ by a series $\sum c_{n} x^{\alpha _{n}}$ with $0 \leq \alpha _{n} \rightarrow \infty$ and $\sum |c_{n}| r^{\alpha _{n}} < \infty$ for some $r>1$ is definable. This expansion is polynomially bounded.
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Additional Information
  • Lou van den Dries
  • Affiliation: University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, Illinois 61801
  • MR Author ID: 59845
  • Email: vddries@math.uiuc.edu
  • Patrick Speissegger
  • Affiliation: University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, Illinois 61801
  • Address at time of publication: Department of Mathematics, University of Toronto, Toronto, Canada M5S 3G3
  • MR Author ID: 361060
  • Email: speisseg@math.utoronto.ca
  • Received by editor(s): April 14, 1996
  • Additional Notes: The first author was supported in part by National Science Foundation Grants No. DMS 95-03398 and INT 92-24546.

    We thank Merton College and the Mathematical Institute of Oxford University for their hospitality during Michaelmas Term 1995.

  • © Copyright 1998 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 350 (1998), 4377-4421
  • MSC (1991): Primary 03C10, 32B05, 32B20; Secondary 26E05
  • DOI: https://doi.org/10.1090/S0002-9947-98-02105-9
  • MathSciNet review: 1458313