论文标题
sublogarithmic-transexponential系列
Sublogarithmic-transexponential series
论文作者
论文摘要
我们适应了Van Den Dries，MacIntyre和Marker的对数指数跨系列的构建，以构建Sublogarithmic-transexponential系列的有序差分领域。我们使用这种结构来构建在组成下关闭的transexpornential hardy场。具体而言，我们证明了$+\ infty $ of $ \ nathcal {l} _ {\ mathrm {transexp}} $ - 单个变量中的术语的细菌，其中$ \ nathcal {l} $ \ MATHCAL {l} _ {\ MATHRM {an}}（\ exp，\ log）$，带有transexponential函数的新符号，其衍生物和其组成倒置。
We adapt the construction of the field of logarithmic-exponential transseries of van den Dries, Macintyre, and Marker to build an ordered differential field of sublogarithmic-transexponential series. We use this structure to build a transexponential Hardy field closed under composition. Specifically, we prove that the germs at $+\infty$ of $\mathcal{L}_{\mathrm{transexp}}$-terms in a single variable are ordered, where $\mathcal{L}_{\mathrm{transexp}}$ is a language containing $\mathcal{L}_{\mathrm{an}}(\exp,\log)$ with new symbols for a transexponential function, its derivatives, and their compositional inverses.
