The exponential rank of non-Archimedean exponential fields

The exponential-logarithmic equivalence classes of surreal numbers

In his monograph, H. Gonshor showed that Conway's real closed field of surreal numbers carries an exponential and logarithmic map. Subsequently, L. van den Dries and P. Ehrlich showed that it is a model of the elementary theory of the field of real numbers with the exponential function. In this paper, we give a complete description of the exponential equivalence classes in the spirit of the classical Archimedean and multiplicative equivalence classes. This description is made in terms of a recursive formula as well as a sign sequence formula for the family of representatives of minimal length …

有序超指数域

Ordered transexponential fields

本研究在含一元函数符号e与T的一阶语言中建立有序超指数域理论，给出有序指数域值群容许相容超指数函数的充要条件，并通过赋值论不变量完全刻画所有可数有序超指数域。

Valuation bases for generalized algebraic series fields

We investigate valued fields which admit a valuation basis. Given a countable ordered abelian group G and a real closed, or algebraically closed field F, we give a sufficient condition for a valued subfield of the field of generalized power series F((G)) to admit a K-valuation basis. We show that the field of rational functions F(G) and the field F(G) of power series in F((G)) algebraic over F(G) satisfy this condition. It follows that for archimedean F and divisible G the real closed field F(G) admits a restricted exponential function.