Algebraic characterization of conflict-free varieties of partial algebras (Q2366148)

In this paper we prove the characterization theorem for particular varieties of partial algebras with weak satisfaction. This problem was studied by many authors, but no general answer has been obtained. Characterizations presented by \textit{H. Höft} [Algebra Univers. 3, 203- 215 (1973; Zbl 0287.08003)] and by \textit{V. S. Poythress} [ibid. 3, 182- 202 (1973; Zbl 0274.08008)] involve conditions for existence of particular algebras rather than those of closure under some operators. The varieties considered by \textit{H. Andréka} and \textit{I. Németi} [``Generalization of the concept of variety and quasivariety to partial algebras through category theory'', Diss. Math. 204 (1983; Zbl 0518.08007)] and by \textit{P. Burmeister} [Algebra Univ. 15, 306-358 (1982; Zbl 0511.03014); A model theoretic oriented approach to partial algebras. Introduction to theory and applications of partial algebras. Part I (1986; Zbl 0598.08004)] are not exactly weak varieties. We have not obtained a general result either, but we suggest another approach to an algebraic characterization. We restrict the class of varieties under consideration instead of adding conditions not involving operators.