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Geometry of interaction. V: Logic in the hyperfinite factor. (English) Zbl 1230.03093
Summary: Geometry of Interaction is a transcendental syntax developed in the framework of operator algebras. This fifth installment of the program takes place inside a von Neumann algebra, the hyperfinite factor. It provides a built-in interpretation of cut elimination as well as an explanation for light, i.e., complexity-sensitive, logics.
For Part IV of this series of papers see [Lect. Notes Log. 24, 76–117 (2006; Zbl 1105.03064)].

MSC:
03F52 Proof-theoretic aspects of linear logic and other substructural logics
03F05 Cut-elimination and normal-form theorems
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