Interpretable fields in real closed valued fields and some expansions

2021/02/01 by Assaf Hasson, Hasson, Assaf, Ya’acov Peterzil +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.2102.00814

openalex publication_date 2021/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathcal M=⟨ K;O⟩ be a real closed valued field and let k be its residue field. We prove that every interpretable field in \mathcal M is definably isomorphic to either K, K(√(-1)), k, or k(√(-1)). The same result holds when K is a model of T, for T an o-minimal power bounded expansion of a real closed field, and O is a T-convex subring. The proof is direct and does not make use of known results about elimination of imaginaries in valued fields.

Citations

• Dp-finite fields II: the canonical topology and its relation to\n henselianity

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