About this product

Product Identifiers

PublisherDover Publications, Incorporated

ISBN-100486450171

ISBN-139780486450179

eBay Product ID (ePID)50809632

Product Key Features

Number of Pages318 Pages

LanguageEnglish

Publication NameBuilding Models by Games

Publication Year2006

SubjectGame Theory, Logic

TypeTextbook

Subject AreaMathematics

AuthorWilfrid Hodges

SeriesDover Books on Mathematics Ser.

FormatPerfect

Dimensions

Item Height0.7 in

Item Weight15 Oz

Item Length9.2 in

Item Width6.7 in

Additional Product Features

Intended AudienceCollege Audience

LCCN2005-055024

Dewey Edition22

IllustratedYes

Dewey Decimal511.3/4

Table Of Content1. Preliminaries2. Games and Forcing3. Existential Closure4. Chaos or Regimentation5. Classical Languages6. Proper Extensions7. Generalised Quantifiers8. L(Q) in Higher CardinalitiesList of types of forcingList of open questionsBibiliographyIndex

SynopsisThis 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., 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.

LC Classification NumberQA9.7.H63 2006