Interpretable fields in real closed valued fields and some expansions

Assaf Hasson; Ya'acov Peterzil

doi:https://doi.org/10.48550/arXiv.2102.00814

Interpretable fields in real closed valued fields and some expansions

Assaf Hasson, Ya'acov Peterzil

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Working paper › Preprint

Abstract

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.

Original language	American English
DOIs	https://doi.org/10.48550/arXiv.2102.00814
State	Published - 7 May 2021

Keywords

Mathematics - Logic

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https://doi.org/10.48550/arXiv.2102.00814

http://adsabs.harvard.edu/abs/2021arXiv210200814H

Cite this

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title = "Interpretable fields in real closed valued fields and some expansions",

abstract = "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.",

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AU - Peterzil, Ya'acov

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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 - https://doi.org/10.48550/arXiv.2102.00814

DO - https://doi.org/10.48550/arXiv.2102.00814

M3 - Preprint

BT - Interpretable fields in real closed valued fields and some expansions

ER -

Interpretable fields in real closed valued fields and some expansions

Abstract

Keywords

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