Nontrivial automorphisms of $\mathcal{P}(\ddot{I}‰)/\mathrm{Fin}$ in Cohen models

Will Brian, Alan Dow

We show that if $\hat{I}º<{\aleph }_{\ddot{I}}‰$ Cohen reals are added to a model of $\mathsf{CH}$, then there are nontrivial automorphisms of $\mathcal{P}(\ddot{I}‰)/\mathrm{Fin}$ in the extension. Under…