Free equivalential algebras
An equivalential algebra is a groupoid \(A=(A,\leftrightarrow )\) that is a subreduct of a Brouwerian semilattice (or, equivalently, a Heyting algebra) with the operation \(\leftrightarrow \) given by \( x\leftrightarrow y=(x\rightarrow y)\wedge (y\rightarrow x).\) This notation was introduced by \textit{J. K. Kabziński} and \textit{A. Wroński} [``On equivalential algebras'', in: Proc. 1975 International Symposium on Multiple-Valued Logic, Indiana Univ., Bloomington, Ind., 1975. Long Beach, Calif.: IEEE Comput. Soc., 419--428 (1975)] as an algebraic counterpart of the equivalential fragment of intuitionistic propositional logic. The class \( \mathcal{E}\) of all equivalential algebras is equationally definable by the following identities: \(xxy=y,xyzz=xz(yz),xy(xzz)(xzz)=xy\). In this paper the author shows how to construct effectively the free finitely generated algebras in \(\mathcal{E}.\)
scientific article; zbMATH DE number 5365118
scientific article