In this paper, we give a self-contained and quite elementary proof that the class of all dimension drop algebras together with their distinguished faithful traces forms a Fraïssé class with the Jiang-Su algebra as its limit. We also show that the UHF algebras can be realized as Fraïssé limits of classes of C*-algebras of matrix-valued continuous functions on [0, 1] with faithful traces.

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.

In this paper, we give a Fraïssé theoretic proof of the result of X. Jiang and H. Su that the Jiang-Su algebra is the unique monotracial simple C*-algebra among all inductive limits of prime dimension drop algebras. The proof presented here is self-contained and quite elementary, and does not depend on any K-theoretic technology. We also partially recover the fact that every unital endomorphism of the Jiang-Su algebra is approximately inner.

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