Continuous model theories for von Neumann algebras

2015/08/13 by Dabrowski, Yoann · 2 citations
#03C20 #03C98 #46L10 #FOS: Mathematics #Logic (math.LO) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1508.03202

Abstract

We axiomatize in (first order finitary) continuous logic for metric structures σ-finite W^*-probability spaces and preduals of von Neumann algebras jointly with a weak-* dense C^*-algebra of its dual. This corresponds to the Ocneanu ultrapower and the Groh ultrapower of (σ-finite in the first case) von Neumann algebras. We give various axiomatizability results corresponding to recent results of Ando and Haagerup including axiomatizability of III_λ factors for 0

Cited by

• Model Theory of General von Neumann Algebras II: Group Actions and Crossed Products
• Model Theory of General von Neumann Algebras I: Generalized Ocneanu Ultraproducts

Related

• An Introduction To Continuous Model Theory
• Model Theory of General von Neumann Algebras I: Generalized Ocneanu Ultraproducts
• Model theory of operator algebras II: Model theory
• Existentially closed W*-probability spaces
• Model theory of C^*-algebras