Anda Latif

On automorphisms of $\mathcal P(λ)/[λ]^{<λ}$

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