TY - UNPB
T1 - Interpretable fields in real closed valued fields and some expansions
AU - Hasson, Assaf
AU - Peterzil, Ya'acov
PY - 2021/5/7
Y1 - 2021/5/7
N2 - 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.
AB - 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.
KW - Mathematics - Logic
U2 - 10.48550/arXiv.2102.00814
DO - 10.48550/arXiv.2102.00814
M3 - Preprint
BT - Interpretable fields in real closed valued fields and some expansions
ER -