Relations Related to Betweenness: Their Structure and Automorphisms (Memoirs of the American Mathematical Society) by S. A. Adeleke (PDF)

Description

This volume is about tree-like structures, namely semilinear ordering, general betweenness relations, $C$-relations and $D$-relations. It contains a systematic study of betweenness and introduces $C$- and $D$-relations to describe the behavior of points at infinity (“leaves” or “ends” or “directions”) of trees. The focus is on structure theorems and on automorphism groups, with applications to the theory of infinite permutation groups. Features: offers the first systematic treatment of betweenness relations introduces important new concepts of $C$-relations and $D$-relations elucidates the close relationships between semilinear orderings, betweenness relations, $C$- and $D$-relations considers their automorphism groups as important examples of Jordan permutation groups

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