Trivial and non-trivial automorphisms of $\mathcal{P} (\omega_1)/[\omega_1]^{<\aleph_0}$

by Shelah and Steprans. [ShSr:1114]
Fundamenta Math, 2018
The following statement is shown to be independent of set theory with the Continuum Hypothesis: There is an automorphism of {P}(omega_1)/[omega_1]^{< aleph_0} whose restriction to {P} (alpha) / [alpha]^{< aleph_0} is induced by a bijection for every alpha in omega_1, but the automorphism itself is not induced by any bijection on omega_1 .

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