Linear Problems in Valued Fields

摘要

A first-order formula over a valued field is called linear if it contains no products or re- ciprocals of quantified variables. We give quantifier elimination procedures based on test term ideas for linear formulas in the following classes of valued fields: discretely valued fields, discretely valued fields with a Z-group as the value group over a language contain- ing predicates stating divisibility in the value group, and non-discretely valued fields.