Open Access
Summer 1995 Classification of Weak De Morgan Algebras
Michiro Kondo
Notre Dame J. Formal Logic 36(3): 396-406 (Summer 1995). DOI: 10.1305/ndjfl/1040149355


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.


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Michiro Kondo. "Classification of Weak De Morgan Algebras." Notre Dame J. Formal Logic 36 (3) 396 - 406, Summer 1995.


Published: Summer 1995
First available in Project Euclid: 17 December 2002

zbMATH: 0835.06012
MathSciNet: MR1351412
Digital Object Identifier: 10.1305/ndjfl/1040149355

Primary: 06D30
Secondary: 03G25

Rights: Copyright © 1995 University of Notre Dame

Vol.36 • No. 3 • Summer 1995
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