Model theory, a major branch of mathematical logic, plays a key role connecting logic and
other areas of mathematics such as algebra, geometry, analysis, and combinatorics …

This dissertation is a collection of results in model theory, related in one way or another to
fields, NIP theories, and elimination of imaginaries. The most important result is a …

$\operatorname {NTP} _ {2} $ is a large class of first-order theories defined by Shelah
generalizing simple and NIP theories. Algebraic examples of $\operatorname {NTP} _ {2} …

We construct a nontrivial definable type V field topology on any dp-minimal field K that is not
strongly minimal, and prove that definable subsets of K n have small boundary. Using this …

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 …

An equation to compute the dp-rank of any abelian group is given. It is also shown that its dp-
rank, or more generally that of any one-based group, agrees with its Vapnik–Chervonenkis …

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 …

Chain conditions in dependent groups - ScienceDirect Skip to main contentSkip to article
Elsevier logo Journals & Books Search RegisterSign in View PDF Download full issue Search …

A field $ K $ in a ring language $\mathcal {L} $ is finitely undecidable if $\mbox
{Cons}(\Sigma) $ is undecidable for every nonempty finite $\Sigma\subseteq\mbox …

In this paper, we show that VC-minimal ordered fields are real closed. We introduce a
notion, strictly between convexly orderable and dp-minimal, that we call dp-small, and show …