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Preprint Number 2051
2051. Mariana Vicaria Elimination of imaginaries in multivalued fields E-mail: Submission date: 16 September 2021 Abstract: In this paper we study elimination of imaginaries in some classes of
henselian valued fields of equicharacteristic zero and residue field
algebraically closed. The results are sensitive to the complexity of the
value
group. We focus first in the case where the ordered abelian group has finite
spines, and then prove a better result for the dp-minimal case. An ordered
abelian with finite spines weakly eliminates imaginaries once we add
sorts for
the quotient groups Γ/Δ for each definable convex subgroup
Δ, and sorts for the quotient groups Γ/Δ+ℓΓ where
Δ is a definable convex subgroup and ℓ in ℕ_{≥ 2}. We
refer to these sorts as the quotient sorts. Mathematics Subject Classification: Keywords and phrases: |

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