The Reconstruction of Trees from Their Automorphism Groups.

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.

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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.