In this talk I will build on the generalized notion of a persistence diagram introduced by A. Patel to multidimensional persistence. I will introduce several lattice-theoretic notions which reduce to known results in the one dimensional parameter case, but generalize to higher dimensional cases. With this interpretation, I will also give a possible definition for a family of distances between diagrams which include the classical bottleneck and wasserstein metrics currently used in applications and time permitting sketch the proof for bottleneck stability for this type of multidimensional persistence.