A non-trivially non-trivial automorphism at an inaccessible cardinal

Abstract

We show that, relative to the existence of an inaccessible cardinal, it is consistent that for an inaccessible cardinal $\kappa$, there is a non-trivial automorphism of $\mathcal{P}(\kappa )/\mathrm{fin}$ whose restriction to $\mathcal{P}(\beta )/\mathrm{fin}$ is induced by a bijection on $\beta$ for every $\beta <\kappa$. This answers questions posed by Larson--McKenney, Shelah--Steprāns, and Veličković.