Hyperseries subfields of surreal numbers

2024/09/24 by Bagayoko, Vincent
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2409.16251

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.

Related

• The hyperserial field of surreal numbers
• Surreal numbers as hyperseries
• The surreal numbers as a universal H-field
• Surreal numbers, exponentiation and derivations
• Surreal fields stable under exponential, logarithmic, derivative and anti-derivative functions