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The Reconstruction of Trees from Their Automorphism Groups
 
The Reconstruction of Trees from Their Automorphism Groups
Softcover ISBN:  978-0-8218-5187-6
Product Code:  CONM/151
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7742-5
Product Code:  CONM/151.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-5187-6
eBook: ISBN:  978-0-8218-7742-5
Product Code:  CONM/151.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
The Reconstruction of Trees from Their Automorphism Groups
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The Reconstruction of Trees from Their Automorphism Groups
Softcover ISBN:  978-0-8218-5187-6
Product Code:  CONM/151
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7742-5
Product Code:  CONM/151.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-5187-6
eBook ISBN:  978-0-8218-7742-5
Product Code:  CONM/151.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 1511993; 274 pp
    MSC: Primary 03; Secondary 20; 06;

    Trees, sometimes called semilinear orders, are partially ordered sets in which every initial segment determined by an element is linearly ordered. This book focuses on automorphism groups of trees, providing a nearly complete analysis of when two trees have isomorphic automorphism groups. Special attention is paid to the class of \(\aleph _0\)-categorical trees, and for this class the analysis is complete. Various open problems, mostly in permutation group theory and in model theory, are discussed, and a number of research directions are indicated. Aimed at graduate students and researchers in model theory and permutation group theory, this self-contained book will bring readers to the forefront of research on this topic.

    Readership

    Graduate students and researchers in model theory and permutation group theory.

  • Table of Contents
     
     
    • Chapters
    • 0. An extended introduction
    • 1. Some preliminaries concerning interpretations, groups and $\aleph _{0}$-categoricity
    • 2. A new reconstruction theorem for Boolean algebras
    • 3. The completion and the Boolean algebra of a U-tree
    • 4. The statement of the canonization and reconstruction theorems
    • 5. The canonization of trees
    • 6. The reconstruction of the Boolean algebra of a U-tree
    • 7. The reconstruction of PT(Exp(M))
    • 8. Final reconstruction results
    • 9. Observations, examples and discussion
    • 10. Augmented trees
    • 11. The reconstruction of $\aleph _{0}$-categorical trees
    • 12. Nonisomorphic 1-homogeneous chains which have isomorphic automorphism groups
    • Bibliography
    • A list of notations and definitions
  • Reviews
     
     
    • The author has made it easy for the interested reader to penetrate this material to any desired depth by providing both a two-page summary and a twenty-seven page introduction. Both of these, as well as the main body of the book, are well motivated, intuitive, and clearly written. The author is obviously sensitive to the readers.

      Mathematical Reviews
  • 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: 1511993; 274 pp
MSC: Primary 03; Secondary 20; 06;

Trees, sometimes called semilinear orders, are partially ordered sets in which every initial segment determined by an element is linearly ordered. This book focuses on automorphism groups of trees, providing a nearly complete analysis of when two trees have isomorphic automorphism groups. Special attention is paid to the class of \(\aleph _0\)-categorical trees, and for this class the analysis is complete. Various open problems, mostly in permutation group theory and in model theory, are discussed, and a number of research directions are indicated. Aimed at graduate students and researchers in model theory and permutation group theory, this self-contained book will bring readers to the forefront of research on this topic.

Readership

Graduate students and researchers in model theory and permutation group theory.

  • Chapters
  • 0. An extended introduction
  • 1. Some preliminaries concerning interpretations, groups and $\aleph _{0}$-categoricity
  • 2. A new reconstruction theorem for Boolean algebras
  • 3. The completion and the Boolean algebra of a U-tree
  • 4. The statement of the canonization and reconstruction theorems
  • 5. The canonization of trees
  • 6. The reconstruction of the Boolean algebra of a U-tree
  • 7. The reconstruction of PT(Exp(M))
  • 8. Final reconstruction results
  • 9. Observations, examples and discussion
  • 10. Augmented trees
  • 11. The reconstruction of $\aleph _{0}$-categorical trees
  • 12. Nonisomorphic 1-homogeneous chains which have isomorphic automorphism groups
  • Bibliography
  • A list of notations and definitions
  • The author has made it easy for the interested reader to penetrate this material to any desired depth by providing both a two-page summary and a twenty-seven page introduction. Both of these, as well as the main body of the book, are well motivated, intuitive, and clearly written. The author is obviously sensitive to the readers.

    Mathematical Reviews
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
Please select which format for which you are requesting permissions.