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ON A GENERALIZED FRAÏSSÉ LIMIT CONSTRUCTION AND ITS APPLICATION TO THE JIANG–SU ALGEBRA

Part of: Linear spaces and algebras of operators Model theory

Published online by Cambridge University Press:  23 October 2020

SHUHEI MASUMOTO
SHUHEI MASUMOTO*
Affiliation:
DEPARTMENT OF GENERAL EDUCATION NATIONAL INSTITUTE OF TECHNOLOGY (KOSEN), KAGAWA COLLEGE 551 KOHDA, TAKUMA-CHO, MITOYO, KAGAWA, JAPANE-mail: [email protected]
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Abstract

In this paper, we present a version of Fraïssé theory for categories of metric structures. Using this version, we show that every UHF algebra can be recognized as a Fraïssé limit of a class of C*-algebras of matrix-valued continuous functions on cubes with distinguished traces. We also give an alternative proof of the fact that the Jiang–Su algebra is the unique simple monotracial C*-algebra among all the inductive limits of prime dimension drop algebras.

Keywords

Fraïssé theoryJiang–Su algebraUHF algebras

MSC classification

Primary: 03C30: Other model constructions
Secondary: 03C98: Applications of model theory 47L40: Limit algebras, subalgebras of $C^*$-algebras
Type
Articles
Information
The Journal of Symbolic Logic , Volume 85 , Issue 3 , September 2020 , pp. 1186 - 1223
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Copyright
© The Association for Symbolic Logic 2020

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References

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