Embeddings into ${\cal P}({\Bbb N})/{\rm fin}$ and extension of automorphisms
Volume 174 / 2002
Fundamenta Mathematicae 174 (2002), 271-284
MSC: Primary 06E99; Secondary 03E35, 03E50, 54G05.
DOI: 10.4064/fm174-3-7
Abstract
Given a Boolean algebra ${\mathbb B}$ and an embedding $e:{\mathbb B}\to {\cal P} ({\mathbb N})/{\rm fin}$ we consider the possibility of extending each or some automorphism of ${\mathbb B}$ to the whole $ {\cal P}({\mathbb N})/{\rm fin}$. Among other things, we show, assuming ${\rm CH}$, that for a wide class of Boolean algebras there are embeddings for which no non-trivial automorphism can be extended.
