Coherent space

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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,TC are said to be orthogonal, written ST, if ST 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 ST for all TF. A coherent space F over C is a family C-sets 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.