对数跨级数域的渐近偶
The Asymptotic Couple of the Field of Logarithmic Transseries
摘要：
在对数跨级数的微分值域$\mathbb{T}_{\log}$上的求导导出其值域群$Γ_{\log}$上的某个映射$ψ$ .结构$(Γ_{\log},ψ)$是一个可分的渐近偶。我们证明了理论$T_{\log} = {\rm Th}(Γ_{\log},ψ)$允许消除量词在一个自然的一阶语言。$T_{\log}$的所有模型$(Γ,ψ)$都有一个重要的离散子集$Ψ:=ψ(Γ\setminus\{0\})$。给出了$Ψ$上所有可定义函数的显式描述，证明了$Ψ$是稳定嵌入$Γ$的.
英文摘要：
The derivation on the differential-valued field $\mathbb{T}_{\log}$ of logarithmic transseries induces on its value group $Γ_{\log}$ a certain map $ψ$. The structure $(Γ_{\log},ψ)$ is a divisible asymptotic couple. We prove that the theory $T_{\log} = {\rm Th}(Γ_{\log},ψ)$ admits elimination of quantifiers in a natural first-order language. All models $(Γ,ψ)$ of $T_{\log}$ have an important discrete subset $Ψ:=ψ(Γ\setminus\{0\})$. We give explicit descriptions of all definable functions on $Ψ$ and prove that $Ψ$ is stably embedded in $Γ$.
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