Boolean algebras admitting a countable minimally acting group (Q2440543)

A group \(H\) of automorphisms of a Boolean algebra \(\mathbb B\) acts minimally on \(\mathbb B\) if for every non-zero \(b\) in \(\mathbb B\) there is a finite subset \(F\) of \(H\) such that \(\bigvee\{h(b):h\in F\}=\mathbf1\). The cardinality of a minimally acting group is at least a large as the Suslin number of the algebra but the authors prove more: If there is a countable group that acts minimally on \(\mathbb B\) then not only is the algebra ccc but it also contains a dense projective subalgebra. The proof constructs a dense subalgebra that satisfies the dual Haydon criterion from [\textit{R. Haydon}, Stud. Math. 52, 23--31 (1974; Zbl 0294.46016)].