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Preprint Number 2297

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2297. Alessandro Linzi, Pierre Touchard
On the hyperfields associated to valued fields

Submission date: 9 November 2022


One can associate to a valued field an inverse system of valued hyperfields (H_i)_{i ∈ I} in a natural way. We investigate when, conversely, such a system arise from a valued field. First, we extend a result of Krasner by showing that the inverse limit of certain systems are stringent valued hyperfields. Secondly, we describe a Hahn-like construction which yields a henselian valued field from a stringent valued hyperfield. In addition, we provide an axiomatisation of the theory of stringent valued hyperfields in a language consisting of two binary function symbols ⊕ and · and two constant symbols 0 and 1.

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Full text arXiv 2211.05082: pdf, ps.

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