Study of a universal formal context

Studying a universal formal context, we obtain a number of properties of the context itself, its concepts, and the lattice formed by the set of these concepts. The most significant of these properties is represented by a theorem showing that there exists an embedding of the concept lattice of an arbitrary at most countable universal context into the concept lattice of a universal context under which the image of the embedding is an initial segment of the concept set of a universal formal context with infinite volumes, and the validity of the dual result. It is shown that the theorem also holds in the computable case. This theorem demonstrates the complexity of the structure of a universal formal context.