Softcover ISBN:  9780821851876 
Product Code:  CONM/151 
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eBook ISBN:  9780821877425 
Product Code:  CONM/151.E 
List Price:  $125.00 
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AMS Member Price:  $100.00 
Softcover ISBN:  9780821851876 
eBook: ISBN:  9780821877425 
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 
Softcover ISBN:  9780821851876 
Product Code:  CONM/151 
List Price:  $130.00 
MAA Member Price:  $117.00 
AMS Member Price:  $104.00 
eBook ISBN:  9780821877425 
Product Code:  CONM/151.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9780821851876 
eBook ISBN:  9780821877425 
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 DetailsContemporary MathematicsVolume: 151; 1993; 274 ppMSC: 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 selfcontained book will bring readers to the forefront of research on this topic.
ReadershipGraduate 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 Utree

4. The statement of the canonization and reconstruction theorems

5. The canonization of trees

6. The reconstruction of the Boolean algebra of a Utree

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 1homogeneous 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 twopage summary and a twentyseven 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


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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 selfcontained book will bring readers to the forefront of research on this topic.
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 Utree

4. The statement of the canonization and reconstruction theorems

5. The canonization of trees

6. The reconstruction of the Boolean algebra of a Utree

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 1homogeneous 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 twopage summary and a twentyseven 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