Algebraic functions in Łukasiewicz implication algebras. (Q2799121)

The authors are concerned with functions definable by conjunctions of equations in the equational class \(K\) of Komori implication algebras, the \(\{\to,1\}\)-subreducts of MV-algebras. When an algebra \(J\) of \(K\) is fixed, the \(J\)-definable functions are said to be algebraic on \(J\). These functions are a step above the term functions of \(J\) in the hierarchy of first order definable functions in the language of \(J\). A characterization is provided of algebraic functions in members of every finitely generated variety of Łukasiewicz implication algebras. A representation theorem is proved for all finite Łukasiewicz implication algebras extending the well known result for Tarski algebras.