The precontraction group of the field of logarithmic transseries $\mathbb{T}_{\log}$
As a first step to understand the theory of the structure $\mathbb{T}_{\log}$ of logarithmic transseries as an ordered valued logarithmic field, we focus on the map $χ$ induced by the logarithm of $\mathbb{T}_{\log}$ in its value group $Γ_{\log}$ and study the theory of the precontraction group $(Γ_{\log},χ)$. Particularly, we show that this theory is model complete and complete, and we characterize all definable subsets of the discrete set $χ(Γ_{\log})$.
math.LO↗