Model Theory

by C. Ward Henson

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Book Description

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.

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).

Table of Contents

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

Book Details

Subject
Mathematics
Publisher
Self-publishing
Published
2010
Pages
122
Edition
1
Language
English
PDF Size
0.7 MB
License
CC BY

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