**Contemporary Mathematics**

Volume: 151;
1993;
274 pp;
Softcover

MSC: Primary 03;
Secondary 20; 06

Print ISBN: 978-0-8218-5187-6

Product Code: CONM/151

List Price: $72.00

Individual Member Price: $57.60

**Electronic ISBN: 978-0-8218-7742-5
Product Code: CONM/151.E**

List Price: $72.00

Individual Member Price: $57.60

# The Reconstruction of Trees from Their Automorphism Groups

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*Matatyahu Rubin*

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.

#### Table of Contents

# Table of Contents

## The Reconstruction of Trees from Their Automorphism Groups

- Contents v6 free
- Summary vii8 free
- 0. An extended introduction 110 free
- 1. Some preliminaries concerning interpretations, groupsand N0 -categoricity 2938
- 2. A new reconstruction theorem for Boolean algebras 4352
- 3. The completion and the Boolean algebra of a U-tree 5766
- 4. The statement of the canonization and reconstruction theorems 6372
- 5. The canonization of trees 7382
- 6. The reconstruction of the Boolean algebra of a U-tree 8796
- 7. The reconstruction of PT(Exp(M)) 135144
- 8. Final reconstruction results 153162
- 9. Observations, examples and discussion 155164
- 10. Augmented trees 169178
- 11. The reconstruction of N0-categorical trees 205214
- 12. Nonisomorphic 1-homogeneous chains which have isomorphic automorphism groups 243252
- Bibliography 251260
- A list of notations and definitions 253262

#### Readership

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

#### 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