Universality on frames

In the present paper we consider so-called saturated classes of frames of weight less than or equal to a given infinite cardinal τ. Such classes are saturated by universal elements. We consider three kinds of saturated classes. The saturated classes of any considered kind have the following basic property: the intersection of not more than τ many saturated classes is also a saturated class and therefore in this intersection there are also universal elements. We prove that the classes RegFrm(τ) of regular and CRegFrm(τ) of completely regular frames of weight ≤τ are saturated classes in any of these kinds. This fact implies that in the classes RegFrm(τ,μ) and CRegFrm(τ,μ) of regular and completely regular frames, respectively, of weight ≤τ and decomposition invariant (see [10]) μ≤τ there are universal elements.