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REDUCED PRODUCTS OF METRIC STRUCTURES: A METRIC FEFERMAN–VAUGHT THEOREM

Published online by Cambridge University Press:  14 September 2016

SAEED GHASEMI
SAEED GHASEMI*
Affiliation:
INSTITUTE OF MATHEMATICS POLISH ACADEMY OF SCIENCES UL. ŚNIADECKICH 8, 00-656 WARSZAWA, POLANDE-mail: sghasemi@impan.pl
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Abstract

We extend the classical Feferman–Vaught theorem to logic for metric structures. This implies that the reduced powers of elementarily equivalent structures are elementarily equivalent, and therefore they are isomorphic under the Continuum Hypothesis. We also prove the existence of two separable C*-algebras of the form ⊕iMk(i) (ℂ) such that the assertion that their coronas are isomorphic is independent from ZFC, which gives the first example of genuinely noncommutative coronas of separable C*-algebras with this property.

Keywords

reduced productsmetric model theorymetric Feferman-Vaught theoremcorona algebrastrivial isomorphisms
Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 3 , September 2016 , pp. 856 - 875
Copyright
Copyright © The Association for Symbolic Logic 2016 

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