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.
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Received: 10 July 2000 ; in final form: 15 April 2002/Published online: 24 February 2003
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ID="*" This paper was written while both authors were partially supported by a Canadian NSERC research grant.
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Kuhlmann, FV., Kuhlmann, S. Valuation theory of exponential Hardy fields I. Math Z 243, 671–688 (2003). https://doi.org/10.1007/s00209-002-0460-4
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DOI: https://doi.org/10.1007/s00209-002-0460-4