Let M=⟨K;O⟩ be a real closed valued field and let k be its residue field. We prove that every interpretable field in 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.
|State||Published - 7 May 2021|
- Mathematics - Logic