Natural Science, Mathematics, 2025
A FUNCTIONAL REPRESENTATION OF FREE DE MORGAN ALGEBRAS
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Submitted: 2025-02-18; Published: 2025-02-18
© 2025 by author(s) and The Gufo Inc.
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(CC BY-NC 4.0).
Abstract
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.