131 research outputs found
Some applications of the ultrapower theorem to the theory of compacta
The ultrapower theorem of Keisler-Shelah allows such model-theoretic notions
as elementary equivalence, elementary embedding and existential embedding to be
couched in the language of categories (limits, morphism diagrams). This in turn
allows analogs of these (and related) notions to be transported into unusual
settings, chiefly those of Banach spaces and of compacta. Our interest here is
the enrichment of the theory of compacta, especially the theory of continua,
brought about by the immigration of model-theoretic ideas and techniques
Fra\"iss\'e limits of C*-algebras
We realize the Jiang-Su algebra, all UHF algebras, and the hyperfinite
II factor as Fra\"iss\'e limits of suitable classes of structures.
Moreover by means of Fra\"iss\'e 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.Comment: 19 pages. Final submitted versio
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