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

RESUMO

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.