Fraïssé limits of C*-algebras

Abstract

We realize the Jiang-Su algebra, all UHF algebras, and the hyperfinite II${}_1$ factor as Fraïssé limits of suitable classes of structures. Moreover by means of Fraïssé theory we provide new examples of AF algebras with strong homogeneity properties. As a consequence of our analysis we deduce Ramsey-theoretic results about the class of full-matrix algebras.

19 pages. Final submitted version

References in corpus (8)

• Nuclear dimension and Z-stability
• Saturation and elementary equivalence of C*-algebras
• Extremely amenable groups via continuous logic
• Logic and operator algebras
• The pseudoarc is a co-existentially closed continuum
• Quantifier elimination in C*-algebras
• A universal nuclear operator system
• Relative commutants of strongly self-absorbing C*-algebras

Cited by in corpus (7)

• Universal AF-algebras
• A universal nuclear operator system
• Strongly self-absorbing $C^{\ast }$-algebras and Fraïssé limits
• Random amenable ${\mathrm{C}}^{\ast }$-algebras
• Twenty years of Nešetřil's classification programme of Ramsey classes
• The Fraïssé limit of matrix algebras with the rank metric
• Expressive power of infinitary [0, 1]-valued logics