in the same way that S4 is a model of interior algebra. Likewise, monadic Boolean algebras supply the algebraic semantics for S5. Hence S5-algebra is a synonym for monadic Boolean algebra. See also Clopen set Cylindric algebra Interior algebra Kuratowski closure axioms Łukasiewicz–Moisil algebra Modal logic Monadic logic References Paul Halmos, 1962. Algebraic Logic. New York: Chelsea. ------ and Steven Givant, 1998. Logic as Algebra. Mathematical Association of America. Algebraic logic Boolean algebra Closure operators