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Super-Boolean Functions and Free Boolean Quasilattices

A Boolean quasilattice is an algebra with hyperidentities of the variety of Boolean algebras. In this paper, we give a functional representation of the free n-generated Boolean quasilattice with two binary, one unary and two nullary operations. Namely, we define the concept of super-Boolean function and prove that the free Boolean quasilattice with two binary, one unary and two nullary operations on n free generators is isomorphic to the Boolean quasilattice of super-Boolean functions of n variables.