Some model theory for generalized trees (Q1825187)

The theory of ordinary trees is embedded by \textit{J. W. Morgan} and \textit{P. B. Shalen} [Ann. Math., II. Ser. 120, 401-476 (1984; Zbl 0583.57005)] and \textit{R. Alperin} and \textit{H. Bass} [Combinatorial Group Theory and Topology, Sel. Pap. Conf., Alta/Utah 1984, Ann. Math. Stud. 111, 265-378 (1987; Zbl 0647.20016)] in a more general theory involving ``metric spaces'' in which the ``distance function'' takes values in an arbitrary ordered Abelian group. First, the left adjoint of the forgetful functor from generalized trees to generalized pretrees is described. Next, a special class of generalized trees, called large trees, is introduced and investigated. Finally, certain model theoretic transfer principles for generalized trees are proved.