Given a Boolean algebra 𝔹 and an embedding e:𝔹 → 𝓟(ℕ)/fin we consider the possibility of extending each or some automorphism of 𝔹 to the whole 𝓟(ℕ)/fin. Among other things, we show, assuming CH, that for a wide class of Boolean algebras there are embeddings for which no non-trivial automorphism can be extended.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm174-3-7, author = {A. Bella and A. Dow and K. P. Hart and M. Hrusak and J. van Mill and P. Ursino}, title = {Embeddings into P(N)/fin and extension of automorphisms}, journal = {Fundamenta Mathematicae}, volume = {173}, year = {2002}, pages = {271-284}, zbl = {1015.06014}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm174-3-7} }
A. Bella; A. Dow; K. P. Hart; M. Hrusak; J. van Mill; P. Ursino. Embeddings into đť“ź(â„•)/fin and extension of automorphisms. Fundamenta Mathematicae, Tome 173 (2002) pp. 271-284. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm174-3-7/