Model theory deals with a branch of mathematical logic showing
connections between a formal language and its interpretations or models.
This is the first and most successful textbook in logical model theory.
Extensively updated and corrected in 1990 to accommodate developments
in model theoretic methods — including classification theory and
nonstandard analysis — the third edition added entirely new sections,
exercises, and references.
Each chapter introduces an individual
method and discusses specific applications. Basic methods of
constructing models include constants, elementary chains, Skolem
functions, indiscernibles, ultraproducts, and special models. The final
chapters present more advanced topics that feature a combination of
several methods. This classic treatment covers most aspects of
first-order model theory and many of its applications to algebra and set
theory.
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Translated from the French, this book is an introduction to first-order
model theory. Starting from scratch, it quickly reaches the essentials,
namely, the back-and-forth method and compactness, which are illustrated
with examples taken from algebra. It also introduces logic via the
study of the models of arithmetic, and it gives complete but accessible
exposition of stability theory.
This is an up-to-date textbook of model theory taking the reader from
first definitions to Morley's theorem and the elementary parts of
stability theory. Besides standard results such as the compactness and
omitting types theorems, it also describes various links with algebra,
including the Skolem-Tarski method of quantifier elimination, model
completeness, automorphism groups and omega-categoricity, ultraproducts,
O-minimality and structures of finite Morley rank. The material on
back-and-forth equivalences, interpretations and zero-one laws can serve
as an introduction to applications of model theory in computer science.
Each chapter finishes with a brief commentary on the literature and
suggestions for further reading. This book will benefit graduate
students with an interest in model theory.
Model theory deals with a branch of mathematical logic showing
connections between a formal language and its interpretations or models.
This is the first and most successful textbook in logical model theory.
Extensively updated and corrected in 1990 to accommodate developments
in model theoretic methods — including classification theory and
nonstandard analysis — the third edition added entirely new sections,
exercises, and references.