Abstract
In this paper we shall first show that for every weak DeMorgan algebra $L(n)$ of order $n$ (WDM-$n$ algebra), there is a quotient weak DeMorgan algebra $L(n){\sim}$ which is embeddable in the finite WDM-$n$ algebra $\Omega (n)$. We then demonstrate that the finite WDM-$n$ algebra $\Omega (n)$ is functionally free for the class $CL(n)$ of WDM-$n$ algebras. That is, we show that any formulas $f$ and $g$ are identically equal in each algebra in $CL(n)$ if and only if they are identically equal in $\Omega (n)$. Finally we establish that there is no weak DeMorgan algebra whose quotient algebra by a maximal filter has exactly seven elements.
Citation
Michiro Kondo. "Classification of Weak De Morgan Algebras." Notre Dame J. Formal Logic 36 (3) 396 - 406, Summer 1995. https://doi.org/10.1305/ndjfl/1040149355
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