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Model theory : an introduction
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
Weakly o-minimal structures and real closed fields
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 introducedExpand
The Elementary Theory of Restricted Analytic Fields with Exponentiation
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 theExpand
Model theory of fields
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 realExpand
Definable Types in O-Minimal Theories
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
Logarithmic-exponential series
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
Degrees of recursively saturated models
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 aExpand
Omitting Types in O-Minimal Theories
  • D. Marker
  • Mathematics, Computer Science
  • J. Symb. Log.
  • 1 March 1986
Model Theory of Differential Fields
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 oneExpand
Introduction to Model Theory
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 beExpand