The class of Krasner hyperfields is not elementary

2024/04/22 by Błaszkiewicz, Piotr, Kowalski, Piotr
#FOS: Mathematics #Logic (math.LO) #Primary 03C60 #Secondary 16Y20

paper · doi:10.48550/arxiv.2404.14532

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.

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