## Notre Dame Journal of Formal Logic

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

### Classification of Weak De Morgan Algebras

#### 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