Hyperseries subfields of surreal numbers

TL;DR

This paper investigates hyperseries subfields of surreal numbers, establishing methods to define embeddings that preserve complex operations like transfinite sums and hyperfunctions, advancing the understanding of surreal number structures.

Contribution

It introduces a framework for hyperseries fields of surreal numbers with compatible derivations and composition laws, including embedding techniques that preserve advanced operations.

Findings

Defined embeddings that commute with transfinite sums

Established compatibility with hyperexponential and hyperlogarithmic functions

Enhanced the structural understanding of hyperseries subfields

Abstract

We study subfields of surreal numbers, called hyperseries fields, that are suited to be equipped with derivations and composition laws. We show how to define embeddings on hyperseries fields that commute with transfinite sums and all hyperexponential and hyperlogarithmic functions.