# zbMATH — the first resource for mathematics

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
Full Text:
##### References:
 [1] Connes, A., Non-commutative geometry, (1994), Academic Press San Diego, CA · Zbl 0933.46069 [2] Fuglede, B.; Kadison, R.V., Determinant theory in finite factors, Annals of mathematics, 2, 55, 520-530, (1952) · Zbl 0046.33604 [3] Girard, J.-Y., Towards a geometry of interaction, (), 69-108 [4] Girard, J.-Y., Geometry of interaction I: interpretation of system $$F$$, (), 221-260 [5] Girard, J.-Y., Geometry of interaction II: deadlock-free algorithms, (), 76-93 [6] Girard, J.-Y., Geometry of interaction III: accommodating the additives, (), 329-389 · Zbl 0828.03027 [7] Girard, J.-Y., Geometry of interaction IV: the feedback equation, (), 76-117 · Zbl 1105.03064 [8] Girard, J.-Y., Locus solum, Mathematical structures in computer science, 11, 301-506, (2001) · Zbl 1051.03045 [9] Girard, J.-Y., Le point aveugle, tome 1: vers la perfection, tome 2: vers !’imperfection, (), 296 pp; 2007, 299 pp [10] Kadison, R. V.; Ringrose, J. R., Fundamentals of the theory of operator algebras, vol. I & II, () · Zbl 0888.46039
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.