Submission date: 4 October 2022

Abstract:

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 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.

Mathematics Subject Classification: 03C60(Primary), 03C52, 03C45, 12J10, 12L12 (Secondary)

Keywords and phrases:

Full text arXiv 2210.01567: pdf, ps.