Original article

Mathematische Zeitschrift

, Volume 243, Issue 4, pp 671-688

First online:

Valuation theory of exponential Hardy fields I

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

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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.