Strict partial orders between ω-trees

Abstract

We consider the set OBT(ω) of the ω -labeled trees ([4]) and the equivalence relation ≃ on this set introduced in [5]. In this paper we define and study a strict partial order ≺ on the set OBT(ω) and a strict partial order ⊏on the factor set OBT(ω)/≃. We characterize these relations and finally we show that t1 ≺ t2 if and only if [t1] ⊏ [t2], where [t] denotes the equivalence class of t.