We will discuss automorphisms of $\mathcal{P}(\lambda)/I_{\kappa}$, for $\kappa \leq \lambda$ infinite cardinals, where $I_{\kappa}$ denotes the ideal of sets of cardinality less than $\kappa$. After surveying what we know about the state of the subject, we will present an argument which shows (among other things) that Martin's Axiom implies that every automorphism of $\mathcal{P}(2^{\aleph_{0}})/Fin$ is trivial off of a countable set. By recent results of Shelah and Steprans, $2^{\aleph_{0}}$ can be replaced here with any cardinal below the least strongly inaccessible.
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