Some model theory for generalized trees
type: Item
instance of: scholarly article
title: Some model theory for generalized trees
zbMATH Open document ID: 0684.03013
DOI: 10.1016/0022-4049(89)90109-6
published in: Journal of Pure and Applied Algebra
publication date: 1989-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 03C60
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 20F60
zbMATH DE Number: 4120156
zbMATH Keywords: generalized metric space
zbMATH Keywords: model complete theory
zbMATH Keywords: left adjoint of the forgetful functor from generalized trees to generalized pretrees
zbMATH Keywords: model theoretic transfer principles
author: Şerban A. Basarab
reviewed by: Şerban A. Basarab
MaRDI profile type: Publication
full work available at URL: 0022-4049(89)90109-6
OpenAlex ID: W2034764386
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description: scientific article; zbMATH DE number 4120156