Contemporary Mathematics 1993; 274 pp; softcover Volume: 151 ISBN10: 082185187X ISBN13: 9780821851876 List Price: US$68 Member Price: US$54.40 Order Code: CONM/151
 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. 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 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 Table of Contents  An extended introduction
 Some preliminaries concerning interpretations, groups and \(\aleph _0\)categoricity
 A new reconstruction theorem for Boolean algebras
 The completion and the Boolean algebra of a Utree
 The statement of the canonization and reconstruction theorems
 The canonization of trees
 The reconstruction of the Boolean algebra of a Utree
 The reconstruction of \(PT({\mathrm Exp}(M))\)
 Final reconstruction results
 Observations, examples and discussion
 Augmented trees
 The reconstruction of \(\aleph _0\)categorical trees
 Nonisomorphic 1homogeneous chains which have isomorphic automorphism groups
 Bibliography
 A list of notations and definitions
