Structure diagrams for primitive Boolean algebras
Abstract: If and are structure diagrams for primitive Boolean algebras, call a homomorphism from onto right-strong iff whenever , there is an such that and ; let RSE denote the category of diagrams and onto right-strong homomorphisms. The relation `` structures '' 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 structures a Boolean algebra recursive in .
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