About: Polyadic algebra

Polyadic algebras (more recently called Halmos algebras) are algebraic structures introduced by Paul Halmos. They are related to first-order logic analogous to the relationship between Boolean algebras and propositional logic (see Lindenbaum–Tarski algebra). There are other ways to relate first-order logic to algebra, including Tarski's cylindric algebras (when equality is part of the logic) and Lawvere's (a categorical approach).