Aronszajn line

In mathematical set theory, an Aronszajn line (named after Nachman Aronszajn) is a linear ordering of cardinality which contains no subset order-isomorphic to * with the usual ordering * the reverse of * an uncountable subset of the Real numbers with the usual ordering. Unlike Suslin lines, the existence of Aronszajn lines is provable using the standard axioms of set theory. A linear ordering is an Aronszajn line if and only if it is the lexicographical ordering of some Aronszajn tree. rdf:langString