We investigate distality and existence of distal expansions in valued fields and related
structures. In particular, we characterize distality in a large class of ordered abelian groups …

This thesis is a study of undecidability in some field theories. Specifically, we are interested
in geometrically oriented problems and have focused our attention in two directions along …

The aim of this article is to give a self-contained account of the algebra and model theory of
Cohen rings, a natural generalization of Witt rings. Witt rings are only valuation rings in case …

A field K in a ring language. We extend a construction of Ziegler and (among other results)
use a first-order classification of Anscombe and Jahnke to prove every NIP henselian …

We prove some results on NIP integral domains, especially those that are Noetherian or
have finite dp-rank. If $ R $ is an NIP Noetherian domain that is not a field, then $ R $ is a …

Given a perfectoid field, we find an elementary extension and a henselian defectless
valuation on it, whose value group is divisible and whose residue field is an elementary …

Let K be an NIP field and let v be a Henselian valuation on K. We ask whether (K, v) is NIP
as a valued field. By a result of Shelah, we know that if v is externally definable, then (K, v) is …

We prove that unstable dp-finite fields admit definable V-topologies. As a consequence, the
henselianity conjecture for dp-finite fields implies the Shelah conjecture for dp-finite fields …

Let $ K $ be an NIP field and let $ v $ be a henselian valuation on $ K $. We ask whether
$(K, v) $ is NIP as a valued field. By a result of Shelah, we know that if $ v $ is externally …

We prove an assortment of results on (commutative and unital) NIP rings, especially 𝔽 p-
algebras. Let R be a NIP ring. Then every prime ideal or radical ideal of R is externally …