Submission date: 22 April 2024

Abstract:

We show that the class of Krasner hyperfields is not elementary. To show this, we determine the rational rank of quotients of multiplicative groups in field extensions. Our argument uses Chebotarev's density theorem. We also discuss some related questions.

Mathematics Subject Classification: Primary 03C60, Secondary 16Y20

Keywords and phrases:

Full text arXiv 2404.14532: pdf, ps.