Extension bases in Henselian valued fields

Akash Hossain

Published 2022-10-04Version 1

We give several sufficient conditions for parameter sets in a Henselian valued field of residue characteristic zero to be an extension base. This enables us in particular to show that forking coincides with dividing in (the $^{eq}$ expansions of) some classical valued fields of residue characteristic zero, like the ultraproducts of the $p$-adic fields, or the field of Laurent series over $\mathbb{C}$. The strategy is to look for easy sufficient conditions for some unary types to be non-forking, and then use a standard induction argument.