In proof theory, a coherent 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. For a family of Csets (i.e., F ⊆ ℘(C)), the dual of F, written F ⊥, is defined as the set of all Csets S such that for every T ∈ F, S ⊥ T. A coherent space F over C is a family Csets for which F = (F ⊥) ⊥.
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