The Reconstruction of Trees from Their Automorphism Groups
1993
American Mathematical Society (Verlag)
9780821851876 (ISBN)
American Mathematical Society (Verlag)
9780821851876 (ISBN)
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Focuses on automorphism groups of trees, providing an analysis of when two trees have isomorphic automorphism groups. This work focuses on the class of $/aleph_0$-categorical trees, and for this class the analysis is complete. It discusses various open problems, mostly in permutation group theory and in model theory.
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.
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.
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 U-tree The statement of the canonization and reconstruction theorems The canonization of trees The reconstruction of the Boolean algebra of a U-tree The reconstruction of $PT({/mathrm Exp}(M))$ Final reconstruction results Observations, examples and discussion Augmented trees The reconstruction of $/aleph_0$-categorical trees Nonisomorphic 1-homogeneous chains which have isomorphic automorphism groups Bibliography A list of notations and definitions.
| Erscheint lt. Verlag | 1.12.1994 |
|---|---|
| Reihe/Serie | Contemporary Mathematics |
| Zusatzinfo | Illustrations |
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 510 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| ISBN-13 | 9780821851876 / 9780821851876 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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