Faithful extensions on finite orders classes

We investigate, in the particular case of finite orders classes, the notion of faithful extensions among relations introduced in 1971 by R. Fraïssé. We show that, for most of the known classes of orders, any order belonging to a class admits a faithful extension also belonging to that class

Faithful extensions on finite orders classes

International audienceIn the particular case of finite orders, we investigate the notion of faithful extension among relations introduced in 1971 by R. Fraısse: an orderQ admits a faithful extension relative to an order P if P does not embed into Q and there exists a strict extension of Q into which P still does not embed. For most of the known order classes, we prove that if P and Q belong to a class then Q admits a faithful extension in this class. For theclass of distributive lattices, we give an infinite family of orders P and Q such that P does not embed into Q and embeds in every strict extension ofQ