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Uncountably Categorical Theories
 
Uncountably Categorical Theories
Hardcover ISBN:  978-0-8218-4586-8
Product Code:  MMONO/117
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4528-7
Product Code:  MMONO/117.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Hardcover ISBN:  978-0-8218-4586-8
eBook: ISBN:  978-1-4704-4528-7
Product Code:  MMONO/117.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
Uncountably Categorical Theories
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Uncountably Categorical Theories
Hardcover ISBN:  978-0-8218-4586-8
Product Code:  MMONO/117
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4528-7
Product Code:  MMONO/117.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Hardcover ISBN:  978-0-8218-4586-8
eBook ISBN:  978-1-4704-4528-7
Product Code:  MMONO/117.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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