The question of whether all automorphisms of $P(\kappa)/fin$ are trivial has been settled in the following cases:

- For $\kappa =\omega$ by Rudin and Shelah

- For $\kappa$ between $\omega_2$ and the first inaccessible by work of Larson & McKenney and Shelah and me.

However the second result hinges on the question for automorphisms of $P(\omega_1)/fin$. I will discuss a resolution to this question stemming from recent work of Shelah and me.