On the structure of nonarchimedean exponential fields I

On the structure of nonarchimedean exponential fields II

In the paper K the second author has studied the structure of nonarchimedean exponential elds i e nonarchimedean ordered elds admitting an order isomor phism between the additive group and the multiplicative group of positive elements Among other results a necessary and su cient criterion was given for countable nonarchimedean elds to be exponential In view of the recent development in the mode...

On the Structure of Nonarchimedean Exponential Elds Ii Franz{viktor and Salma Kuhlmann

Constructible exponential functions, motivic Fourier transform and transfer principle

We introduce spaces of exponential constructible functions in the motivic setting for which we construct direct image functors in the absolute and relative settings. This allows us to define a motivic Fourier transformation for which we get various inversion statements. We also define spaces of motivic Schwartz-Bruhat functions on which motivic Fourier transformation induces isomorphisms. Our m...

NSM 2006 Nonstandard Methods Congress , Pisa

• Since Wilkie’s result [9] (which established that the elementary theory Texp of (R, exp) is model complete and o-minimal), many o-minimal expansions of the reals have been investigated. The problem of constructing nonarchimedean models of Texp (and more generally, of an ominimal expansion of the reals) gained much interest. • In [2] it was shown that fields of generalized power series cannot ...

A ug 1 99 7 The exponential rank of nonarchimedean exponential fields

Based on the work of Hahn, Baer, Ostrowski, Krull, Kaplansky and the Artin-Schreier theory, and stimulated by the paper [L] of S. Lang in 1953, the theory of real places and convex valuations has witnessed a remarkable development and has become a basic tool in the theory of ordered fields and real algebraic geometry. Surveys on this development can be found in [LAM] and [PC]. In this paper, we...