Dimension and universality on frames

In this paper we first introduce the notion of a saturated class of frames and then define a dimension-like invariant of a frame, the so-called decomposition invariant denoted by dec, which is a cardinal (in particular maybe a non-negative integer), and using the notion of the saturated class prove that in the class of all frames of weight less than or equal to a fixed infinite cardinal τ having decomposition invariant ≤μ, where μ is a fixed cardinal less than or equal to τ, there are universal elements.