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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/
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Abstract

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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

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