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The Classification of Countable Homogeneous Directed Graphs and Countable Homogeneous $n$-tournaments
 
Gregory L. Cherlin :  Rutgers University, New Brunswick, NJ
The Classification of Countable Homogeneous Directed Graphs and Countable Homogeneous n-tournaments
eBook ISBN:  978-1-4704-0210-5
Product Code:  MEMO/131/621.E
List Price: $57.00
MAA Member Price: $51.30
AMS Member Price: $34.20
Add to cart
The Classification of Countable Homogeneous Directed Graphs and Countable Homogeneous n-tournaments
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The Classification of Countable Homogeneous Directed Graphs and Countable Homogeneous $n$-tournaments
Gregory L. Cherlin :  Rutgers University, New Brunswick, NJ
eBook ISBN:  978-1-4704-0210-5
Product Code:  MEMO/131/621.E
List Price: $57.00
MAA Member Price: $51.30
AMS Member Price: $34.20
Add to cart
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 131; 1998; 161 pp
    MSC: Primary 05; Secondary 03; 20

    In this book, Ramsey theoretic methods introduced by Lachlan are applied to classify the countable homogeneous directed graphs. This is an uncountable collection, and this book presents the first explicit classification result covering an uncountable family. The author's aim is to demonstrate the potential of Lachlan's method for systematic use.

    Features:

    • Interface between combinatorics and model theory
    • Unusual use of Ramsey's theorem to classify structures
    • An extension of an already elaborate branch of model theory
    • The first monograph on Lachlan's method
    Readership

    Graduate students and mathematicians interested in model theory, combinatorics, infinite permutation and group theory.
  • Table of Contents
     
     
    • Chapters
    • 1. Results and open problems
    • 2. Homogeneous 2-tournaments
    • 3. Homogeneous $n$-tournaments
    • 4. Homogeneous symmetric graphs
    • 5. Homogeneous directed graphs omitting $I_\infty $
    • 6. Propositions 16 to 20 and MT 2.2
    • 7. Homogeneous directed graphs embedding $I_\infty $
    • 8. Theorems 7.6-7.9
  • 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
Memoirs of the American Mathematical Society
Volume: 131; 1998; 161 pp
MSC: Primary 05; Secondary 03; 20

In this book, Ramsey theoretic methods introduced by Lachlan are applied to classify the countable homogeneous directed graphs. This is an uncountable collection, and this book presents the first explicit classification result covering an uncountable family. The author's aim is to demonstrate the potential of Lachlan's method for systematic use.

Features:

  • Interface between combinatorics and model theory
  • Unusual use of Ramsey's theorem to classify structures
  • An extension of an already elaborate branch of model theory
  • The first monograph on Lachlan's method
Readership

Graduate students and mathematicians interested in model theory, combinatorics, infinite permutation and group theory.
  • Chapters
  • 1. Results and open problems
  • 2. Homogeneous 2-tournaments
  • 3. Homogeneous $n$-tournaments
  • 4. Homogeneous symmetric graphs
  • 5. Homogeneous directed graphs omitting $I_\infty $
  • 6. Propositions 16 to 20 and MT 2.2
  • 7. Homogeneous directed graphs embedding $I_\infty $
  • 8. Theorems 7.6-7.9
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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