On the simplicity of the automorphism group of \(\mathcal P (\omega )\)/fin (Q1204121)

Since the automorphism group of any saturated Boolean algebra is simple - -- the saturation here is meant in model theoretic sense ---, the automorphism group of \({\mathcal P}(\omega)/\text{fin}\) is simple under CH. In contrast, van Dowen showed that the automorphism group of \({\mathcal P}(\omega)/\text{fin}\) is non-simple if every automorphism of \({\mathcal P}(\omega)/\text{fin}\) is almost trivial (this is the case e.g. under \(\text{MA}_{\aleph_ 1}+\text{OCA}\) (Veličković)). In the paper it is proved that the simplicity of the automorphism group of \({\mathcal P}(\omega)/\text{fin}\) is preserved if we start from a model of CH and add \(\aleph_ 2\) Cohen reals.