Some model theory for generalized trees
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.
left adjoint of the forgetful functor from generalized trees to generalized pretrees
scientific article; zbMATH DE number 4120156