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    The Bone Clocks

    David Mitchell 9781400065677

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Building Models by Games:

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Synopses & Reviews

Publisher Comments:

This volume presents research by algebraists and model theorists in accessible form for advanced undergraduates or beginning graduate students studying algebra, logic, or model theory. It introduces a general method for building infinite mathematical structures and surveys applications in algebra and model theory. A multi-step procedure, the method resembles a two-player game that continues indefinitely. This approach simplifies, motivates, and unifies a wide range of constructions.

Starting with an overview of basic model theory, the text examines a variety of algebraic applications, with detailed analyses of existentially closed groups of class 2. It describes the classical model-theoretic form of this method of construction, which is known as "omitting types," "forcing," or the "Henkin-Orey theorem," The final chapters are more specialized, discussing how the idea can be used to build uncountable structures. Applications include completeness for Magidor-Malitz quantifiers, Shelah's recent and sophisticated omitting types theorem for L(Q), and applications to Boolean algebras and models of arithmetic. More than 160 exercises range from elementary drills to research-related items, with further information and examples.

Synopsis:

This volume introduces a general method for building infinite mathematical structures and surveys applications in algebra and model theory. It covers basic model theory and examines a variety of algebraic applications, including completeness for Magidor-Malitz quantifiers, Shelah's recent and sophisticated omitting types theorem for L(Q), and applications to Boolean algebras. Over 160 exercises. 1985 edition.

Table of Contents

1. Preliminaries

2. Games and Forcing

3. Existential Closure

4. Chaos or Regimentation

5. Classical Languages

6. Proper Extensions

7. Generalised Quantifiers

8. L(Q) in Higher Cardinalities

List of types of forcing

List of open questions

Bibiliography

Index

Product Details

ISBN:
9780486450179
Author:
Hodges, Wilfrid
Publisher:
Dover Publications
Author:
Mathematics
Subject:
Logic
Subject:
Game Theory
Subject:
Model theory
Subject:
Mathematics-Modeling
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Publication Date:
20060431
Binding:
TRADE PAPER
Language:
English
Illustrations:
Y
Pages:
336
Dimensions:
9.25 x 6.13 in 0.93 lb

Related Subjects


Science and Mathematics » Mathematics » Foundations and Logic
Science and Mathematics » Mathematics » Geometry » Algebraic Geometry
Science and Mathematics » Mathematics » Logic and Philosophy
Science and Mathematics » Mathematics » Modeling

Building Models by Games: New Trade Paper
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Product details 336 pages Dover Publications - English 9780486450179 Reviews:
"Synopsis" by ,
This volume introduces a general method for building infinite mathematical structures and surveys applications in algebra and model theory. It covers basic model theory and examines a variety of algebraic applications, including completeness for Magidor-Malitz quantifiers, Shelah's recent and sophisticated omitting types theorem for L(Q), and applications to Boolean algebras. Over 160 exercises. 1985 edition.

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