Towards a Model Theory for Transseries

TL;DR

This paper explores the algebraic and model-theoretic properties of the differential field of transseries, aiming to understand its first-order theory and its applications in various mathematical contexts.

Contribution

It provides an overview of the algebraic and model-theoretic aspects of transseries and reports on ongoing efforts to analyze its first-order theory.

Findings

Transseries extend real Laurent series and appear in diverse mathematical areas.

The paper advances understanding of the first-order theory of transseries.

It highlights the relevance of transseries in asymptotic analysis and o-minimal structures.

Abstract

The differential field of transseries extends the field of real Laurent series, and occurs in various context: asymptotic expansions, analytic vector fields, o-minimal structures, to name a few. We give an overview of the algebraic and model-theoretic aspects of this differential field, and report on our efforts to understand its first-order theory.