Compatible Tight Riesz Orders on the Group of Automorphisms of an 0-2-Homogeneous Set: Addendum

Abstract

The purpose of this note is to show that Theorem 8 of Davis and Fox [1] is sharp. That is, we show that the following result is valid.THEOREM. Let Ω be an 0-2-homogeneous ordered set. Then Tρ(respectively, Tƛ ) is a maximal compatible tight Riesz order if and only if Ω has a countable cofinal(respectively, coinitial) subset.