Surreal numbers, exponentiation and derivations

TL;DR

This paper explores the structure of Conway's surreal numbers, emphasizing their relationships with transseries and Hardy fields, and aims to simplify existing theoretical frameworks.

Contribution

It provides a clearer presentation of surreal numbers with a focus on their connections to transseries and Hardy fields, streamlining previous complex treatments.

Findings

Established links between surreal numbers and transseries.

Simplified the theoretical framework of surreal numbers.

Enhanced understanding of Hardy fields in relation to surreal numbers.

Abstract

We give a presentation of Conway's surreal numbers focusing on the connections with transseries and Hardy fields and trying to simplify when possible the existing treatments.