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The Reconstruction of Trees from Their Automorphism Groups

About this Title

Matatyahu Rubin

Publication: Contemporary Mathematics
Publication Year: 1993; Volume 151
ISBNs: 978-0-8218-5187-6 (print); 978-0-8218-7742-5 (online)
DOI: https://doi.org/10.1090/conm/151
MathSciNet review: 1240317

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Table of Contents

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Front/Back Matter

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Chapters

• 0. An extended introduction
• 1. Some preliminaries concerning interpretations, groups and $\aleph _{0}$-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 $\aleph _{0}$-categorical trees
• 12. Nonisomorphic 1-homogeneous chains which have isomorphic automorphism groups
• Bibliography
• A list of notations and definitions