Cylindric algebra

Summary

A cylindric algebra is a Boolean algebra with extra operations that model existential quantifiers and constants that model equality of variables. Alfred Tarski and his collaborators introduced them to do for predicate logic with equality what Boolean algebras do for propositional logic. The cylindrification $c_\kappa$ plays the role of "there exists $x_\kappa$", and the diagonal element $d_{\kappa\lambda}$ plays the role of the formula $x_\kappa = x_\lambda$.