标题： Hardy域上的常数幂映射和拟幂级数 显示英文标题

标题： Constant power maps on Hardy fields and transseries

摘要： 设$\mathbb{T}$为对数-指数超实数微分域。 我们考虑通过将实数$r$和正超实数$f$映射到超实数$f^r$的二元映射对$\mathbb{T}$的扩展。 基于 Aschenbrenner、van den Dries 和 van der Hoeven 的最新工作，我们证明该扩展是模型完备的，并给出了该扩展理论的有效公理化，相对于实指数域的理论而言。 我们证明，配备相同映射$(f,r)\mapsto f^r$的极大 Hardy 域与$\mathbb{T}$拥有相同的理论，并利用此来建立 Hardy 域与超实数之间的传递定理。 显示英文摘要

摘要： Let $\mathbb{T}$ be the differential field of logarithmic-exponential transseries. We consider the expansion of $\mathbb{T}$ by the binary map that sends a real number $r$ and a positive transseries $f$ to the transseries $f^r$. Building on recent work of Aschenbrenner, van den Dries, and van der Hoeven, we show that this expansion is model complete, and we give an axiomatization of the theory of this expansion that is effective relative to the theory of the real exponential field. We show that maximal Hardy fields, equipped with the same map $(f,r)\mapsto f^r$, enjoy the same theory as $\mathbb{T}$, and we use this to establish a transfer theorem between Hardy fields and transseries.