We introduce quantum Boolean algebras which are the analogue of the Weyl algebras for Boolean affine spaces.We study quantum Boolean algebras from the logical and the set theoretical viewpoints.

Let D = (V, A) be a finite simple directed graph (shortly digraph). A function f : V −→ {−1, 1} is called a twin signed dominating function (TSDF) if f(N −[v]) > 1 and f(N +[v]) > 1 for each vertex v ∈ V . The twin signed ...