Submission date: 1 February 2024

Abstract:

We introduce an elementary class of linearly ordered groups, called growth order groups, encompassing certain groups under composition of formal series (e.g. transseries) as well as certain groups 𝒢_ℳ of infinitely large germs at infinity of unary functions definable in an o-minimal structure ℳ. We study the algebraic structure of growth order groups and give methods for constructing examples. We show that if ℳ expands the real ordered field and germs in 𝒢_ℳ are levelled in the sense of Marker & Miller, then 𝒢_ℳ is a growth order group.

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Full text arXiv 2402.00549: pdf, ps.