**by C. Ward Henson**

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The purpose of the book is to give a thorough introduction to the methods of model theory for first order logic. Model theory is the branch of logic that deals with mathematical structures and the formal languages they interpret. First order logic is the most important formal language and its model theory is a rich and interesting subject with significant applications to the main body of mathematics. Model theory began as a serious subject in the 1950s with the work of Abraham Robinson and Alfred Tarski, and since then it has been an active and successful area of research.

Beyond the core techniques and results of model theory, this book places a lot of emphasis on examples and applications, in order to show clearly the variety of ways in which model theory can be useful in mathematics. For example, we give a thorough treatment of the model theory of the field of real numbers (real closed fields) and show how this can be used to obtain the characterization of positive semi-definite rational functions that gives a solution to Hilbert's 17th Problem. ### Table of Contents

### Book Details

### Related Books

Beyond the core techniques and results of model theory, this book places a lot of emphasis on examples and applications, in order to show clearly the variety of ways in which model theory can be useful in mathematics. For example, we give a thorough treatment of the model theory of the field of real numbers (real closed fields) and show how this can be used to obtain the characterization of positive semi-definite rational functions that gives a solution to Hilbert's 17th Problem.

This open book is licensed under a Creative Commons License (CC BY). You can download Model Theory ebook for free in PDF format (0.7 MB).

Chapter 1

Ultraproducts and the Compactness Theorem

Chapter 2

Theories and Types

Chapter 3

Elementary Maps

Chapter 4

Saturated Models

Chapter 5

Quantifier Elimination

Chapter 6

Löwenheim-Skolem Theorems

Chapter 7

Algebraically Closed Fields

Chapter 8

Z-groups

Chapter 9

Model Theoretic Algebraic Closure

Chapter 10

Algebraic Closure in Minimal Structures

Chapter 11

Real Closed Ordered Fields

Chapter 12

Homogeneous Models

Chapter 13

Omitting Types

Chapter 14

ω-categoricity

Chapter 15

Skolem Hulls

Chapter 16

Indiscernibles

Chapter 17

Morley rank and ω-stability

Chapter 18

Morley's uncountable categoricity theorem

Chapter 19

Characterizing Definability

Title

Model Theory

Subject

Science and Mathematics

Publisher

Self-publishing

Published

2010

Pages

122

Edition

1

Language

English

PDF Size

0.7 MB

License

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