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${\mathcal {P}}(\lambda )/[\lambda ]^{<\lambda }$
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 $.
