Notre Dame Journal of Formal Logic

Classification of Weak De Morgan Algebras

Michiro Kondo

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.

Article information

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

Dates
First available in Project Euclid: 17 December 2002

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1040149355

Digital Object Identifier
doi:10.1305/ndjfl/1040149355

Mathematical Reviews number (MathSciNet)
MR1351412

Zentralblatt MATH identifier
0835.06012

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

Citation

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


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References

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  • Rasiowa, H., An Algebraic Approach to Non-Classical Logics, North-Holland, Amsterdam, 1974. Zbl 0299.02069 MR 56:5285