## 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.## References

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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