Interpretable fields in real closed valued fields and some expansions

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 $K$, $K(\sqrt{-1})$, $k$, or $k(\sqrt{-1})$. 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.

References in corpus (2)

• Dp-finite fields II: the canonical topology and its relation to henselianity
• Dp-finite fields VI: the dp-finite Shelah conjecture

Cited by in corpus (2)

• Fields interpretable in $P$-minimal fields
• Notes on trace equivalence