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Preprint Number 718

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718. Allen Gehret
The Asymptotic Couple of the Field of Logarithmic Transseries

Submission date: 5 May 2014.


The derivation on the differential-valued field 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} = Th(Γ_{log},ψ) admits elimination of quantifiers in a natural first-order language. All models (Γ_{log},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.

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Full text arXiv 1405.1012: pdf, ps.

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