A minimal Kurepa line

Abstract

We show it is consistent with $\ZFC$ that there is an everywhere Kurepa line which is order isomorphic to all of its dense ${\aleph }_2$-dense suborders. Moreover, this Kurepa line does not contain any Aronszajn suborder. We also show it is consistent with $\ZFC$ that there is a minimal Kurepa line which does not contain any Aronszajn suborder.