# Aronszajn line

In mathematical set theory, an Aronszajn line (named after Nachman Aronszajn) is a linear ordering of cardinality ${\displaystyle \aleph _{1}}$ which contains no subset order-isomorphic to
• ${\displaystyle \omega _{1}}$ with the usual ordering
• the reverse of ${\displaystyle \omega _{1}}$