The Asymptotic Couple of the Field of Logarithmic Transseries

2014/05/05 by Gehret, Allen
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1405.1012

Abstract

The derivation on the differential-valued field \mathbbT_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∖\0\). We give explicit descriptions of all definable functions on Ψ and prove that Ψ is stably embedded in Γ.

Related

• NIP for the Asymptotic Couple of the Field of Logarithmic Transseries
• The precontraction group of the field of logarithmic transseries \mathbbT_log
• Dimension theory for the asymptotic couple of the field of logarithmic transseries
• Revisiting closed asymptotic couples
• Tame pairs of transseries fields