文摘
The derivation on the differential-valued field Tlog of logarithmic transseries induces on its value group Γlog a certain map ψ . The structure (Γlog,ψ) is a divisible asymptotic couple. We prove that the theory Tlog=Th(Γlog,ψ) admits elimination of quantifiers in a natural first-order language. All models 3297cb8a52cd22ef5a39e80b02ea5a" title="Click to view the MathML source">(Γ,ψ) of Tlog 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.