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Uncountably Categorical Theories
 
Front Cover for Uncountably Categorical Theories
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Hardcover ISBN: 978-0-8218-4586-8
Product Code: MMONO/117
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Product Code: MMONO/117.E
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Uncountably Categorical Theories
Available Formats:
Hardcover ISBN:  978-0-8218-4586-8
Product Code:  MMONO/117
List Price: $66.00
MAA Member Price: $59.40
AMS Member Price: $52.80
Electronic ISBN:  978-1-4704-4528-7
Product Code:  MMONO/117.E
List Price: $62.00
MAA Member Price: $55.80
AMS Member Price: $49.60
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
  • Book Details
     
     
    Translations of Mathematical Monographs
    Volume: 1171993; 122 pp
    MSC: Primary 03; 05;

    The 1970s saw the appearance and development in categoricity theory of a tendency to focus on the study and description of uncountably categorical theories in various special classes defined by natural algebraic or syntactic conditions. There have thus been studies of uncountably categorical theories of groups and rings, theories of a one-place function, universal theories of semigroups, quasivarieties categorical in infinite powers, and Horn theories. In Uncountably Categorical Theories, this research area is referred to as the special classification theory of categoricity. Zilber's goal is to develop a structural theory of categoricity, using methods and results of the special classification theory, and to construct on this basis a foundation for a general classification theory of categoricity, that is, a theory aimed at describing large classes of uncountably categorical structures not restricted by any syntactic or algebraic conditions.

    Readership

    Research mathematicians.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • Chapter 1. Survey of preliminary results and terminology
    • Chapter 2. Three types of uncountably categorical structures
    • Chapter 3. Classification of infinite locally finite homogeneous pregeometries
    • Chapter 4. Description of strongly minimal quasi-algebras
    • Chapter 5. Global structure of uncountable categorical structures
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Volume: 1171993; 122 pp
MSC: Primary 03; 05;

The 1970s saw the appearance and development in categoricity theory of a tendency to focus on the study and description of uncountably categorical theories in various special classes defined by natural algebraic or syntactic conditions. There have thus been studies of uncountably categorical theories of groups and rings, theories of a one-place function, universal theories of semigroups, quasivarieties categorical in infinite powers, and Horn theories. In Uncountably Categorical Theories, this research area is referred to as the special classification theory of categoricity. Zilber's goal is to develop a structural theory of categoricity, using methods and results of the special classification theory, and to construct on this basis a foundation for a general classification theory of categoricity, that is, a theory aimed at describing large classes of uncountably categorical structures not restricted by any syntactic or algebraic conditions.

Readership

Research mathematicians.

  • Chapters
  • Introduction
  • Chapter 1. Survey of preliminary results and terminology
  • Chapter 2. Three types of uncountably categorical structures
  • Chapter 3. Classification of infinite locally finite homogeneous pregeometries
  • Chapter 4. Description of strongly minimal quasi-algebras
  • Chapter 5. Global structure of uncountable categorical structures
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