Transseries and Todorov-Vernaeve's asymptotic fields

TL;DR

This paper explores the connection between transseries fields and residue fields in non-standard real extensions, addressing a question posed by Todorov and Vernaeve.

Contribution

It establishes a relationship between transseries fields and residue fields of convex subrings in non-standard analysis, providing an answer to Todorov and Vernaeve's question.

Findings

Identifies the link between transseries and residue fields in non-standard models

Provides a new understanding of the structure of asymptotic fields

Answers a specific open question in the field

Abstract

We study the relationship between fields of transseries and residue fields of convex subrings of non-standard extensions of the real numbers. This was motivated by a question of Todorov and Vernaeve, answered in this paper.