Structure diagrams for primitive Boolean algebras

If S S and T T are structure diagrams for primitive Boolean algebras, call a homomorphism f f from S S onto T T right-strong iff whenever x T f ( t ) xTf(t) , there is an s s such that f ( s ) = x f(s) = x and s S t sSt ; let RSE denote the category of diagrams and onto right-strong homomorphisms. The relation “ S S structures B B ” between diagrams and Boolean algebras induces a 1-1 correspondence between the components of RSE and the isomorphism types of primitive Boolean algebras. Up to isomorphism, each component of RSE contains a unique minimal diagram and a unique maximal tree diagram. The minimal diagrams are like those given in a construction by William Hanf. The construction which is given for producing maximal tree diagrams is recursive; as a result, every diagram S S structures a Boolean algebra recursive in S S .