Aronszajn Free Kurepa Trees

We consider a transitive relation on the power set of ${\omega }_1$ and show if there is a maximal element with respect to this relation then there is a Kurepa tree with no Aronszajn subtree. We also show that if there is a maximal subset of ${\omega }_1$, then there are Kurepa trees which are not club isomorphic. These maximal subsets of ${\omega }_1$ exist in many known models that are obtained from the constructible universe without large cardinal assumptions. For instance, whenever ${\alpha }_0\in {\omega }_1$ and $X\subset {\omega }_1$ are such that $\omega_1^{$\text{textsc}L$[X \cap \alpha_0]} = \omega_1, \omega_2^{$\text{textsc}L$[X]} = \omega_2$and$$\text{textsc}V$$isasemiproperforcingextensionof$$\text{textsc}L$[X]$then$X$ismaximalin$$\text{textsc}V$$.