Trivial and non-trivial automorphisms of $\mathcal P(\omega _1)/[\omega _1]^{<\aleph _0}$
Volume 243 / 2018
Fundamenta Mathematicae 243 (2018), 155-168
MSC: 03E20, 03E35, 03G05.
DOI: 10.4064/fm402-11-2017
Published online: 27 June 2018
Abstract
The following statement is shown to be independent of set theory with the Continuum Hypothesis: There is an automorphism of $\mathcal P(\omega _1)/[\omega _1]^{ \lt \aleph _0}$ whose restriction to $\mathcal P(\alpha )/[\alpha ]^{ \lt \aleph _0}$ is induced by a bijection for every $\alpha \in \omega _1$, but the automorphism itself is not induced by any bijection on $\omega _1$.
