TY  - BOOK
AU  - Rubin,Matatyahu
TI  - The Reconstruction of Trees from Their Automorphism Groups
T2  - Contemporary Mathematics Series
SN  - 9780821877425
AV  - QA9.7 .R83 1993 
U1  - 511/.5 
PY  - 1993///
CY  - Providence
PB  - American Mathematical Society
KW  - Model theory
KW  - Automorphisms
KW  - Trees (Graph theory)
KW  - Electronic books
N1  - Intro -- Contents -- Summary -- 0. An extended introduction -- 1. Some preliminaries concerning interpretations, groupsand N0 -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 N0-categorical trees -- 12. Nonisomorphic 1-homogeneous chains which have isomorphic automorphism groups -- Bibliography -- A list of notations and definitions
N2  - 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
UR  - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5295190
ER  -