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ON THE AXIOMATIZABILITY OF C*-ALGEBRAS AS OPERATOR SYSTEMS
Published online by Cambridge University Press: 19 September 2018
Abstract
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.
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- Copyright © Glasgow Mathematical Journal Trust 2018