论文标题
力量很容易避免
Powers are easy to avoid
论文作者
论文摘要
假设$ \ wideTilde {\ mathbb r} $是实际字段的o最小扩展，其中限制功率函数是可以定义的。 We show that if $\widehat{\mathbb R}$ is both a reduct (in the sense of definability) of the expansion $\widetilde{\mathbb R}^{\mathbb R}$ of $\widetilde{\mathbb R}$ by all real power functions and an expansion (again in the sense of definability) of然后，如果$ \ mathbb r} $，前提是$ \ wideTilde {\ mathbb r} $和$ \ wideHat {\ mathbb r} $具有相同的指数字段，它们定义了相同的集合。这可以看作是van den dries and Miller的旧猜想的多项式有限版。
Suppose that $\widetilde{\mathbb R}$ is an o-minimal expansion of the real field in which restricted power functions are definable. We show that if $\widehat{\mathbb R}$ is both a reduct (in the sense of definability) of the expansion $\widetilde{\mathbb R}^{\mathbb R}$ of $\widetilde{\mathbb R}$ by all real power functions and an expansion (again in the sense of definability) of $\widetilde{\mathbb R}$, then, provided that $\widetilde{\mathbb R}$ and $\widehat{\mathbb R}$ have the same field of exponents, they define the same sets. This can be viewed as a polynomially bounded version of an old conjecture of van den Dries and Miller.
