Coherent space

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 ^⊥) ^⊥.

In Proofs and Types coherent spaces are called coherence spaces. A footnote explains that although in the French original they were espaces cohérents, the coherence space translation was used because spectral spaces are sometimes called coherent spaces.