ON AUTOMORPHISMS OF P(λ)/[λ]<λ

We investigate the statement "all automorphisms of $\mathcal P(\lambda)/[\lambda]^{\lt \lambda}$ are trivial using set theory. We first show that MA imples the statement for regular uncountable cardinals $\lamba < 2^{\aleph_0}$ and the statement is false for measurable $\lambda$ if $2^\lamba =\lambda^{+}$. Then we construct a creature forcing to show that for "densly trivial", the statement can be forced for inaccesible cardinals $\lambda$ (together with $2^{\lambda}=\lambda^{++}$