Limits of k-dimensional poset sequences

In 2011, Janson (2011) extended the theory of graph limits to posets, defining convergence for poset sequences and proving that every such sequence has a limit object. In this paper, we focus on k-dimensional poset sequences. This restriction leads to shorter proofs and to a more intuitive limit object. As before, the limit object can be used as a model for random posets, which generalizes the well known random k-dimensional poset model. Furthermore, it can also be used to characterize a natural class of testable poset parameters.