March 12
Hossein Lamei Ramandi, University of Toronto
Galvin's question on non-$\sigma$-well ordered linear orders

Assume $\mathcal{C}$ is the class of all linear orders $L$ such that $L$ is not a countable union of well ordered sets, and every uncountable subset of $L$ contains a copy of $\omega_1$. We show it is consistent that $\mathcal{C}$ has minimal elements. This answers an old question due to Galvin.