Automorphisms of $\mathcal{P}(\lambda )/{\mathcal{I}}_{\kappa }$

Abstract

We study conditions on automorphisms of Boolean algebras of the form $P(\lambda )/I_{\kappa }$ (where $\lambda$ is an uncountable cardinal and $I_{\kappa }$ is the ideal of sets of cardinality less than $\kappa$) which allow one to conclude that a given automorphism is trivial. We show (among other things) that every cardinality-preserving automorphism of $P(2^{\kappa })/I_{{\kappa }^{+}}$ which is trivial on all sets of cardinality ${\kappa }^{+}$ is trivial, and that $M{A}_{{\aleph }_1}$ implies that every automorphism of $P(\mathbb{R})/Fin$ is trivial on a cocountable set.

arXiv comment23 pages