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 tau having decomposition invariant <= mu, where mu is a fixed cardinal less than or equal to tau, there are universal elements. (C) 2015 Elsevier B.V. All rights reserved.