Abstract
This article treats the determination of the largest powerset lattice that can be order embedded into a complete lattice \(\mathbb {L}\). That’s a complexity measure for \(\mathbb {L}\) and can be seen as an inner dimension. We show that this embedding problem translates to a set packing problem on the level of formal contexts. From this point of view, similarities to graph theoretic parameters emerge, which lead to a lattice theoretical interpretation of the clique number of simple graphs, in terms of an inner dimension of complete ortholattices. Furthermore, behaviour of the tensor product of complete (ortho)lattices is studied w.r.t. these inner dimensions.
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