On the proof of elimination of imaginaries in algebraically closed valued fields

Abstract

We give a simplified proof of elimination of imaginaries (in the geometric sorts) in ACVF, based on ideas of Hrushovski. This proof manages to avoid many of the technical issues which arose in the original proof by Haskell, Hrushovski, and Macpherson.

New and improved coding for finite sets (section 4.3)

Cited by in corpus (3)

• Around definable types in $p$-adically closed fields
• Some definable types that cannot be amalgamated
• Imaginaries in equicharacteristic zero henselian fields