Dp-minimal valued fields
Franziska Jahnke, Pierre Simon, Erik Walsberg
TL;DR
This paper investigates the structure of dp-minimal valued fields, establishing their henselian property and classifying dp-minimal ordered abelian groups and fields, revealing their algebraic and topological characteristics.
Contribution
It proves that dp-minimal valued fields are henselian and classifies dp-minimal ordered structures, providing new insights into their algebraic and topological properties.
Findings
Dp-minimal valued fields are henselian.
A dp-minimal field with a definable type V topology is either real closed, algebraically closed, or has a non-trivial definable henselian valuation.
Classifications of dp-minimal ordered abelian groups and fields are provided.
Abstract
We show that dp-minimal valued fields are henselian and that a dp-minimal field admitting a definable type V topology is either real closed, algebraically closed or admits a non-trivial definable henselian valuation. We give classifications of dp-minimal ordered abelian groups and dp-minimal ordered fields without additional structure.
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