## 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

https://projecteuclid.org/euclid.ndjfl/1040149355

Digital Object Identifier
doi:10.1305/ndjfl/1040149355

Mathematical Reviews number (MathSciNet)
MR1351412

Zentralblatt MATH identifier
0835.06012

#### 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

#### References

• Kondo, M., “Representation theorem of quasi-Kleene algebras in terms of Kripke-type frames," Mathematica Japonica, vol. 38 (1993), pp. 185–189. Zbl 0771.06004 MR 94a:06028
• Rasiowa, H., An Algebraic Approach to Non-Classical Logics, North-Holland, Amsterdam, 1974. Zbl 0299.02069 MR 56:5285