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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The real field with convergent
generalized power series


Authors: Lou van den Dries and Patrick Speissegger
Journal: Trans. Amer. Math. Soc. 350 (1998), 4377-4421
MSC (1991): Primary 03C10, 32B05, 32B20; Secondary 26E05
MathSciNet review: 1458313
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Abstract | References | Similar Articles | Additional Information

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
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
Email: speisseg@math.utoronto.ca

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02105-9
PII: S 0002-9947(98)02105-9
Keywords: o-minimal structures, model completeness, power series, blowing-up
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.<P> We thank Merton College and the Mathematical Institute of Oxford University for their hospitality during Michaelmas Term 1995.
Article copyright: © Copyright 1998 American Mathematical Society



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