Notre Dame Journal of Formal Logic

Classification of Weak De Morgan Algebras

Michiro Kondo


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.

Article information

Notre Dame J. Formal Logic, Volume 36, Number 3 (1995), 396-406.

First available in Project Euclid: 17 December 2002

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 06D30: De Morgan algebras, Lukasiewicz algebras [See also 03G20]
Secondary: 03G25: Other algebras related to logic [See also 03F45, 06D20, 06E25, 06F35]


Kondo, Michiro. Classification of Weak De Morgan Algebras. Notre Dame J. Formal Logic 36 (1995), no. 3, 396--406. doi:10.1305/ndjfl/1040149355.

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