Models and Ultraproducts
Title | Models and Ultraproducts PDF eBook |
Author | John Lane Bell |
Publisher | Courier Corporation |
Pages | 338 |
Release | 2006-01-01 |
Genre | Mathematics |
ISBN | 0486449793 |
In this text for first-year graduate students, the authors provide an elementary exposition of some of the basic concepts of model theory--focusing particularly on the ultraproduct construction and the areas in which it is most useful. The book, which assumes only that its readers are acquainted with the rudiments of set theory, starts by developing the notions of Boolean algebra, propositional calculus, and predicate calculus. Model theory proper begins in the fourth chapter, followed by an introduction to ultraproduct construction, which includes a detailed look at its theoretic properties. An overview of elementary equivalence provides algebraic descriptions of the elementary classes. Discussions of completeness follow, along with surveys of the work of Jónsson and of Morley and Vaught on homogeneous universal models, and the results of Keisler in connection with the notion of a saturated structure. Additional topics include classical results of Gödel and Skolem, and extensions of classical first-order logic in terms of generalized quantifiers and infinitary languages. Numerous exercises appear throughout the text.
Models and Ultraproducts
Title | Models and Ultraproducts PDF eBook |
Author | A. B. Slomson |
Publisher | Dover Publications |
Pages | 336 |
Release | 2013-12-20 |
Genre | |
ISBN | 9780486788630 |
This first-year graduate text assumes only an acquaintance with set theory to explore homogeneous universal models, saturated structure, extensions of classical first-order logic, and other topics. 1974 edition.
Models and Ultraproducts
Title | Models and Ultraproducts PDF eBook |
Author | John Lane Bell |
Publisher | |
Pages | 322 |
Release | 1971 |
Genre | Model theory |
ISBN |
Models and Ultraproducts
Title | Models and Ultraproducts PDF eBook |
Author | John Lane Bell |
Publisher | |
Pages | 344 |
Release | 1971 |
Genre | Mathematics |
ISBN |
The aim of this book is to provide an elementary exposition of some of the basic concepts of model theory. Model theory, which can be described briefly as the study of the relationship between formal languages and abstract structures, covers a very wide field and it is not possible to compress it into one volume. We have chosen as our theme the ultraproducts construction. We hope this book we be of use to undergraduate and practicing mathematicians.
Ultraproducts in the Theory of Models
Title | Ultraproducts in the Theory of Models PDF eBook |
Author | Simon Bernard Kochen |
Publisher | |
Pages | 0 |
Release | 1961 |
Genre | |
ISBN |
Model Theory
Title | Model Theory PDF eBook |
Author | |
Publisher | |
Pages | 0 |
Release | 1973 |
Genre | Model theory |
ISBN | 9780720422009 |
A Shorter Model Theory
Title | A Shorter Model Theory PDF eBook |
Author | Wilfrid Hodges |
Publisher | Cambridge University Press |
Pages | 322 |
Release | 1997-04-10 |
Genre | Mathematics |
ISBN | 9780521587136 |
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.