A FUNCTIONAL REPRESENTATION OF FREE DE MORGAN ALGEBRAS - Movsisyan, Yu.M. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2022)
It is well known that free Boolean algebra on n free generators is isomorphic to the Boolean algebra of Boolean functions of n variables. The free distributive lattice on n free generators is isomorphic to the lattice of monotone Boolean functions of n variables. In this paper we introduce the concept of De Morgan function and prove that the free De Morgan algebra on n free generators is isomorphic to the De Morgan algebra of De Morgan functions of n variables. Keywords: Antichain, monotone Boolean function, De Morgan function, free De Morgan algebra.
Keywords: Antichain; monotone Boolean function; De Morgan function; free De Morgan algebra