Most algebras have the interpolation property (Q1272139)

For an algebra \(\mathcal U\) let \(L_{\kappa } P(\mathcal U)\) be the set of all \(\kappa \)-local polynomial functions (i.e. functions which can be interpolated by a polynomial on any set of \(<\kappa\) many points). In the paper under review the author gives a criterion to decide, for regular \(\kappa \), when there are algebras \(\mathcal U\) satisfying the \(\kappa \)-interpolation property (i.e.\ for which \(L_1 P(\mathcal U) = L_{\kappa }P(\mathcal U)\)). He also shows that if one algebra on the underlying set \(A\) has the \(\kappa \)-interpolation property, then also ``almost all'' algebras have this property.