具有无理power function和稠密乘法子群的实域
The real field with an irrational power function and a dense multiplicative subgroup
摘要：
本文提供了第一个例子的模型理论上表现良好的结构组成的一个适当的o-最小的实域的扩展和有限秩的稠密乘法子群。在一定的Schanuel条件下，给出了实域上具有无理幂函数和有限秩的稠密乘法子群的量词消去结果，该稠密乘法子群的元素在无理幂生成的域上是代数的.而且，在这个结构中可定义的每一个开集在由实域和无理幂函数给出的约简中已经是可定义的。
英文摘要：
This paper provides a first example of a model theoretically well behaved structure consisting of a proper o-minimal expansion of the real field and a dense multiplicative subgroup of finite rank. Under certain Schanuel conditions, a quantifier elimination result will be shown for the real field with an irrational power function and a dense multiplicative subgroup of finite rank whose elements are algebraic over the field generated by the irrational power. Moreover, every open set definable in this structure is already definable in the reduct given by just the real field and the irrational power function.
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