This book is a modern introduction to model theory which stresses applications to algebra throughout the text. The first half of the book includes classical material on model construction techniques,… Expand

A linearly ordered structure is weakly o-minimal if all of its definable sets in one variable are the union of finitely many convex sets in the structure. Weakly o-minimal structures were introduced… Expand

numbers with exponentiation is model complete. When we combine this with Hovanskii's finiteness theorem [9], it follows that the real exponential field is o-minimal. In o-minimal expansions of the… Expand

The model theory of fields is an area for important interactions between mathematical, logical and classical mathematics. Recently, there have been major applications of model theoretic ideas to real… Expand

The goal is to provide a characterization of definable types over r-minimal structures that generalizes van den Dries' results and shows that every type over an M- minimal expansion -of R is definable.Expand

Evidence is given for the conjecture that the field of LE-series is a universal domain for ordered differential algebra in Hardy fields, and its basic properties are established, including the existence of compositional inverses.Expand

Using relativizations of results of Goncharov and Peretyat'kin on decidable homogeneous models, we prove that if M is S-saturated for some Scott set S, and F is an enumeration of S, then M has a… Expand

This article surveys the model theory of differentially closed fields, an interesting setting where one can use model-theoretic methods to obtain algebraic information. The article concludes with one… Expand

This article introduces some of the basic concepts and results from model theory, starting from scratch. The topics covered are be tailored to the model theory of fields and later articles. I will be… Expand