The asymptotic couple of the field of logarithmic transseries

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• 作者：Allen Gehret ^{agehret2@illinois.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Asymptotic couples ; Logarithmic transseries ; Quantifier elimination
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：470
• 期：Complete
• 页码：1-36
• 全文大小：605 K

文摘

The derivation on the differential-valued field T_log${\mathbb{T}}_{\log }$ of logarithmic transseries induces on its value group Γ_log${\mathrm{\Gamma }}_{\log }$ a certain map ψ  . The structure (Γ_log,ψ)$({\mathrm{\Gamma }}_{\log },\psi )$ is a divisible asymptotic couple. We prove that the theory T_log=Th(Γ_log,ψ)$T_{\log }=\mathrm{Th}({\mathrm{\Gamma }}_{\log },\psi )$ admits elimination of quantifiers in a natural first-order language. All models (Γ,ψ)$(\mathrm{\Gamma },\psi )$ of T_log$T_{\log }$ have an important discrete subset Ψ:=ψ(Γ∖{0})$\mathrm{\Psi }:=\psi (\mathrm{\Gamma }\setminus \{0\})$. We give explicit descriptions of all definable functions on Ψ and prove that Ψ is stably embedded in Γ.