NSM 2006 Nonstandard Methods Congress , Pisa
نویسنده
چکیده
• 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 admit an exponential function. • Elaborationg on an idea of [3], we construct in [4] fields of generalized power series with support of bounded cardinality which admit an exponential. • In this talk, we present the construction given in [4]: We give a natural definition of an exponential, which makes these fields into models of the o-minimal expansion Tan,exp := the theory of the reals with restricted analytic functions and exponentiation. •We present preliminary ideas on how to introduce derivation operators on these models. The aim is to present a new class of ordered differential fields, with many interesting properties.
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