Coherent space (original) (raw)

In proof theory, a coherent space (also coherence space) is a concept introduced in the semantic study of linear logic. Let a set C be given. Two subsets S,T ⊆ C are said to be orthogonal, written S ⊥ T, if S ∩ T is ∅ or a singleton. The dual of a family F ⊆ ℘(C) is the family F ⊥ of all subsets S ⊆ C orthogonal to every member of F, i.e., such that S ⊥ T for all T ∈ F. A coherent space F over C is a family of C-subsets for which F = (F ⊥) ⊥.