Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4583571 | Journal of Algebra | 2017 | 36 Pages |
Abstract
The derivation on the differential-valued field TlogTlog of logarithmic transseries induces on its value group ΓlogΓlog a certain map ψ . The structure (Γlog,ψ)(Γlog,ψ) is a divisible asymptotic couple. We prove that the theory Tlog=Th(Γlog,ψ)Tlog=Th(Γlog,ψ) admits elimination of quantifiers in a natural first-order language. All models (Γ,ψ)(Γ,ψ) of TlogTlog have an important discrete subset Ψ:=ψ(Γ∖{0})Ψ:=ψ(Γ∖{0}). We give explicit descriptions of all definable functions on Ψ and prove that Ψ is stably embedded in Γ.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Allen Gehret,