… The main result of this paper is that a dp-minimal valued field is henselian. As a
consequence, we show that an ℵ1-saturated dp-minimal ordered field admits a henselian …

… (2018), we classify the pure fields and pure valued fields of dp-rank 1, … dp-minimal fields.
Specializing to the case of dp-small fields, we prove that dp-small fields and VC-minimal fields …

… The author would like to thank Nick Ramsey for informing him of Jahnke, Simon and
Walsberg’s work on dp-minimal valued fields, and Tom Scanlon for helping review an earlier …

… Let (K, v) be a henselian defectless valued field with algebraically closed residue field and
value group Γ. Suppose Γ/nΓ is finite for all n. If the residue characteristic is p > 0, suppose …

… of dp-minimal fields and dp-minimal valuation rings. We show that if R is a dp-minimal integral
domain, then R is a field or a valuation … : there is a dp-minimal valuation overring O ⊇ R, a …

… Finally we establish that the field of p-adic numbers is dp-minimal. … valued fields are dp-minimal
by showing that, more generally, VC-minimal theories (for which see [2]) are dp-minimal. …

… We continue our local analysis of groups interpretable in various dp-minimal valued fields,
as introduced in [8]. We associate with every infinite group G interpretable in those fields an …

… henselian valuations on a dp-minimal real field. Additionally we characterise all dpminimal
real fields that admit a definable henselian valuation with real closed residue field. We do so …

… that dp-minimal expansions of discretely valued fields are “… × → Z is a non-trivial discrete
valuation on K, and K is an … Dpminimal valued fields are Henselian [21], so we suppose …

… is positive for a dp-minimal field by the results of Johnson [14] (so under the assumptions of
Theorem 1.4, we have that K is dp-minimal if and only if both k and Γ are dp-minimal), but the …