Density conditions for quantum propositions

Density conditions for quantum propositions

As has already been pointed out by Birkhoff and von Neumann, quantum logic can be formulated in terms of projective geometry. In three-dimensional Hilbert space, elementary logical propositions are associated with one-dimensional subspaces, corresponding to points of the projective plane. It is shown that, starting with three such propositions corresponding to some basis {~u,~v, ~ w}, successiv...

Density onditions for quantum propositions

Physical propositions and quantum languages

The word proposition is used in physics with different meanings, which must be distinguished to avoid interpretational problems. We construct two languages L∗(x) and L(x) with classical set-theoretical semantics which allow us to illustrate those meanings and to show that the nonBoolean lattice of propositions of quantum logic (QL) can be obtained by selecting a subset of p-testable proposition...

Sufficient Conditions for Density in Extended Lipschitz Algebras

Density Conditions For Triangles In Multipartite Graphs

We consider the problem of finding a large or dense triangle-free subgraph in a given graph G. In response to a question of P. Erdős, we prove that, if the minimum degree of G is at least 17|V (G)|/20, the largest triangle-free subgraphs are precisely the largest bipartite subgraphs in G. We investigate in particular the case where G is a complete multipartite graph. We prove that a finite trip...