Résumé | The ternary betweenness relation on a tree, B(x,y,z), indicates that y is on the unique path between x and z. This notion can be extended to order-theoretic trees defined as partial orders such that the set of nodes greater than any node is linearly ordered. In such generalized trees, the unique "path" between two nodes can have infinitely many nodes. We axiomatize in first-order or monadic second-order logic several betweenness relations in order-theoretical trees. |