Homogeneous Boolean algebras with very nonsymmetric subalgebras (Q788717)

This paper considers the question of when automorphisms of Boolean subalgebras extend. Inverting the usual point of view, under \(\diamond\) a complete homogeneous Souslin algebra is constructed with a complete subalgebra moved by every nontrivial automorphism of the Souslin algebra. Extending the question to endomorphisms, for every Boolean algebra A homogeneous extensions \(C\supseteq B\supseteq A\) are found where every automorphism or endomorphism of A extends to B and no one-one endomorphism or automorphism of B extends to C. The proofs given are rather sketchy, requiring more than the usual familiarity with the literature.