Submission date: 5 June 2012.

Abstract:

A preliminary version of this manuscript had appeared as [1]. The material of the first 3 sections was subsequently published as [2]. The material of sections 4 and 5 appeared in [3]. The rest of the material was never published. As it seems to be still of interest, we have decided to make the manuscript available on the arxiv in its original form.

We describe the residue fields of arbitrary convex valuations on certain o-minimal expansions of the ordered field of real numbers. References: [1] Franz-Viktor and Salma Kuhlmann: Residue fields of arbitrary convex valuations on restricted analytic fields with exponentiation I, The Fields Institute Preprint Series (1997). [2] Franz-Viktor and Salma Kuhlmann: Valuation theory of exponential Hardy fields I, Mathematische Zeitschrift 243, 671--688 (2003) [3] Ordered Exponential Fields, by Salma Kuhlmann, The Fields Institute Monograph Series Vol. 12, (2000).

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Full text arXiv 1206.0711: pdf, ps.