 In general, the axiomatization of products of modal logics is a delicate issue, and some interesting phenomena can arise.  For instance, the two-dimensional modal product logic S5\(\,\times\,\)S5 has a finite axiomatization but, for \(n \geq 3\), the \(n\)-dimensional product logic S5\(^{n}\) is non-finitely axiomatizable. In Kurucz and Marcelino 2012 there were found the first examples of decidable two-dimensional products of finitely axiomatizable modal logics, such as K4.3\(\,\times\,\)S5, which fail to be finitely axiomatizable. These are examples of logics that fall prey to what we may call the finite crash phenomenon, where the finite axiomatizability property is destroyed under the action of products. 