标题： 可定义的几乎实闭域秩 显示英文标题

标题： Definable ranks of almost real closed fields

摘要： 我们引入有序域、有序阿贝尔群和有序集的可定义秩的概念。 我们研究有序域的可定义秩与其自然赋值值群的可定义秩之间的关系。 类似地，我们将有序阿贝尔群的可定义秩与它的自然赋值值集进行比较。 我们特别考虑几乎实闭域的情形，并给出在域、值群和值集层面上的可定义秩相等的条件。 显示英文摘要

摘要： We introduce the notion of the definable rank of an ordered field, ordered abelian group and ordered set, respectively. We study the relation between the definable rank of an ordered field and the definable rank of the value group of its natural valuation. Similarly we compare the definable rank of an ordered abelian group and the value set of its natural valuation. We consider in particular the case of an almost real closed field and give conditions under which the definable ranks on the level of field, of value group and of value set coincide.