Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-10T16:15:04.950Z Has data issue: false hasContentIssue false
  • English
  • Français

ON THE AXIOMATIZABILITY OF C*-ALGEBRAS AS OPERATOR SYSTEMS

Published online by Cambridge University Press:  19 September 2018

ISAAC GOLDBRING  and
THOMAS SINCLAIR
ISAAC GOLDBRING*
Affiliation:
Department of Mathematics, University of California, Irvine, 340 Rowland Hall (Bldg.# 400), Irvine, CA 92697-3875, USA e-mail: isaac@math.uci.edu URL: http://www.math.uci.edu/isaac
THOMAS SINCLAIR*
Affiliation:
Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907-2067, USA e-mail: tsincla@purdue.edu URL: http://www.math.purdue.edu/tsincla/
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We show that the class of unital C*-algebras is an elementary class in the language of operator systems and that the algebra multiplication is a definable function in this language. Moreover, we prove a general model theoretic fact which implies that the aforementioned class is ∀∃∀-axiomatizable. We conclude by showing that this class is, however, neither ∀∃-axiomatizable nor ∃∀-axiomatizable.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 61 , Issue 3 , September 2019 , pp. 629 - 635
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

REFERENCES

Ben, I. Yaacov, A. Berenstein, C. W. Henson and Usvyatsov, A., Model theory for metric structures, in Model theory with applications to algebra and analysis (London Math. Soc. Lecture Note Ser. (350)). 2, (Cambridge Univ. Press, Cambridge, 2008), 315–427.CrossRefGoogle Scholar
Blecher, D. and Neal, M., Metric characterizations II, Illinois J. Math. 57 (2013), 25–41.CrossRefGoogle Scholar
Elliott, G., Farah, I., Paulsen, V., Rosendal, C., Toms, A. and Tornquist, A., The isomorphism relation for separable C*-algebras, Math. Res. Lett. 20 (2013), 1071–1080.CrossRefGoogle Scholar
Farah, I., Hart, B., Lupini, M., Robert, L., Tikuisis, A., Vignati, A. and Winter, W., The model theory of nuclear C* algebras, Mem. Amer. Math. Soc., to appear.Google Scholar
Farah, I., Hart, B. and Sherman, D., Model theory of operator algebras II: Model theory, Israel J. Math. 201 (2014), 477–505.CrossRefGoogle Scholar
Goldbring, I. and Lupini, M., Model theoretic aspects of the Gurarij operator system, Israel J. Math. 226 (1) (2018), 87–118.CrossRefGoogle Scholar
Goldbring, I. and Sinclair, T., On Kirchberg's embedding problem, J. Funct. Anal. 269 (2015), 155–198.CrossRefGoogle Scholar