, Volume 243, Issue 4, pp 671-688

Valuation theory of exponential Hardy fields I

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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.

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.