Imaginaries in Boolean algebras (Q2888634)

Special kinds of equivalence relations on powers of a Boolean algebra are introduced, and elimination of imaginaries is proved for the associated multisorted structure. Two new ideas are involved: restricted elementary invariants, which are a simple modfication of the usual Tarski invariants, and the notion of largeness. \(a\) is large in \(b\) iff for every natural number \(n\), \(a\cdot b\in I_n\) iff \(b\in I_n\), where \(I_n\) is the \(n\)-th invariant. The main theorem is a rather technical result concerning largeness.