Maximal Chains of Copies of the Rational Line

Abstract

We show that the class of order types of maximal chains in the partial order \(\langle E(\mathbb Q)\cup \{\emptyset \}, \subset \rangle\), where \(E(\mathbb Q)\) is the set of all subsets X of the rational line, \({\mathbb Q}\), such that X with the inherited order is isomorphic to \({\mathbb Q}\), is exactly the class of order types of compact sets of reals having the minimum non-isolated.