Model Theory
by C. Ward Henson
DescriptionTable of ContentsDetailsHashtagsReport an issue
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. 
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
Title
Model Theory
Subject
Science and Mathematics
Publisher
Self-publishing
Published
2010
Pages
122
Edition
1
Language
English
PDF Size
0.7 MB
License
Related Books
This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability...
Late in a career of more than sixty years, Thomas Burch, an internationally known social demographer, undertook a wide-ranging methodological critique of demography. This open access volume contains a selection of resulting papers, some previously unpublished, some published but not readily accessible [from past meetings of The International Union...
With this graduate-level primer, the principles of the standard model of particle physics receive a particular skillful, personal and enduring exposition by one of the great contributors to the field. In 2013 the late Prof. Altarelli wrote: The discovery of the Higgs boson and the non-observation of new particles or exotic phenomena have made a big...
The overarching aim of this book is to present self-contained theory and algorithms for investigation and prediction of electric demand peaks. A cross-section of popular demand forecasting algorithms from statistics, machine learning and mathematics is presented, followed by extreme value theory techniques with examples.In order to achieve carbon t...
This open access brief introduces the basic principles of control theory in a concise self-study guide. It complements the classic texts by emphasizing the simple conceptual unity of the subject. A novice can quickly see how and why the different parts fit together. The concepts build slowly and naturally one after another, until the reader soon ha...
This book examines the methodological complications of using complexity science concepts within the social science domain. The opening chapters take the reader on a tour through the development of simulation methodologies in the fields of artificial life and population biology, then demonstrates the growing popularity and relevance of these method...