Interpretable fields in real closed valued fields and some expansions

Assaf Hasson; Ya'acov Peterzil

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arXiv · 2102.00814

Interpretable fields in real closed valued fields and some expansions

Assaf Hasson·Ya'acov Peterzil

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Abstract

Let $\mathcal M=\langle K;O\rangle$ 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.

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BibTeX RIS

Assaf Hasson, Ya'acov Peterzil. 2021-02-01. Interpretable fields in real closed valued fields and some expansions. https://arxiv.org/abs/2102.00814

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