  We investigate the statement ``all automorphisms of $\mathcal
P(\lambda)/[\lambda]^{<\lambda}$ are trivial''. We show that MA implies the
statement for regular uncountable $\lambda<2^{\aleph_0}$; that the statement is
false for measurable $\lambda$ if $2^\lambda=\lambda^+$; and that for ``densely
trivial'' it can be forced (together with $2^\lambda=\lambda^{++}$) for
inaccessible $\lambda$.
