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Model theory of operator algebras II: model theory

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Abstract

We introduce a version of logic for metric structures suitable for applications to C*-algebras and tracial von Neumann algebras. We also prove a purely model-theoretic result to the effect that the theory of a separable metric structure is stable if and only if all of its ultrapowers associated with nonprincipal ultrafilters on ℕ are isomorphic even when the Continuum Hypothesis fails.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, York University, 4700 Keele Street, North York, Ontario, Canada, M3J 1P3

    Ilijas Farah

  2. Matematicki Institut, Kneza Mihaila 34, Belgrade, Serbia

    Ilijas Farah

  3. Department of Mathematics and Statistics, McMaster University, 1280 Main Street, West Hamilton, Ontario, Canada, L8S 4K1

    Bradd Hart

  4. Department of Mathematics, University of Virginia, P. O. Box 400137, Charlottesville, VA, 22904-4137, USA

    David Sherman

Authors
  1. Ilijas Farah
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  2. Bradd Hart
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  3. David Sherman
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Corresponding author

Correspondence to Ilijas Farah.

Additional information

The first two authors are partially supported by NSERC.

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Farah, I., Hart, B. & Sherman, D. Model theory of operator algebras II: model theory. Isr. J. Math. 201, 477–505 (2014). https://doi.org/10.1007/s11856-014-1046-7

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  • DOI: https://doi.org/10.1007/s11856-014-1046-7

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