Archimedean actions on median pretrees

In this paper we consider group actions on generalized treelike structures (termed 'pretrees') defined simply in terms of betweenness relations. risin g a result of Levitt, me show that; if a countable group admits an archimed ean action on a median pretree, then it admits an action by isometries on a n PS-tree. Thus the theory of isometric actions on IR-trees may be extended to a more general setting where it merges naturally with the theory of rig ht-orderable groups. This approach has application also to the study of con vergence group actions on continua.