Mathematische Zeitschrift

, Volume 243, Issue 4, pp 671–688

Valuation theory of exponential Hardy fields I

Authors

  • Franz-Viktor Kuhlmann
    • Mathematical Sciences Group, University of Saskatchewan, 106 Wiggins Road, Saskatoon, Saskatchewan, Canada S7N 5E6 (e-mail: {fvk;skuhlman}@math.usask.ca)
  • Salma Kuhlmann
    • Mathematical Sciences Group, University of Saskatchewan, 106 Wiggins Road, Saskatoon, Saskatchewan, Canada S7N 5E6 (e-mail: {fvk;skuhlman}@math.usask.ca)
Original article

DOI: 10.1007/s00209-002-0460-4

Cite this article as:
Kuhlmann, F. & Kuhlmann, S. Math Z (2003) 243: 671. doi:10.1007/s00209-002-0460-4

Abstract.

We describe the valuation theoretic properties of the Hardy fields associated to models of \(T(\exp)\), where T is the theory of a polynomially bounded o-minimal expansion of the reals and \(\exp\) is the real exponential function. We deduce that \(T(\exp)\) has levels with parameters and is exponentially bounded. We establish a maximality property of \(H(\mathbb{R}_{\rm an, powers})\), the Hardy field of the expansion by the restricted analytic functions and power functions.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003