Power of a set of equationally complete submanifolds of a manifold of symmetrically ternary quasigroups

Abstract

Manifolds of algebras with the operation xyzτ defined by the following identities: 1) xyzτ yzτ=x; 2) xxyzτ zτ=y; 3) xyxyzτ τ=z; 4) xxzτ =z, which correspond to Steiner quadruplets [3], like manifolds of structures, have a unique equationally complete submanifold [4]. It is proved that in the class of all algebras defined only by the identities 1), 2), and 3) the set of all equationally complete submanifolds has the power of a continuum.