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- In the 14th IEEE International Conference on Distributed Computing Systems (OPODIS94
, 1994

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### OMITTING TYPES IN OPERATOR SYSTEMS

"... Abstract. We show that the class of 1-exact operator systems is not uniformly definable by a sequence of types. We use this fact to show that there is no finitary version of Arveson’s extension theorem. Next, we show that WEP is equivalent to a certain notion of existential closed-ness for C ∗ algeb ..."

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Abstract. We show that the class of 1-exact operator systems is not uniformly definable by a sequence of types. We use this fact to show that there is no finitary version of Arveson’s extension theorem. Next, we show that WEP is equivalent to a certain notion of existential closed-ness for C ∗ algebras and use this equivalence to give a simpler proof of Kavruk’s result that WEP is equivalent to the complete tight Riesz interpolation property. We then introduce a variant of the space of n-dimensional operator systems and connect this new space to the Kirch-berg Embedding Problem, which asks whether every C ∗ algebra embeds into an ultrapower of the Cuntz algebra O2. We end with some results concerning the question of whether or not the local lifting property (in the sense of Kirchberg) is uniformly definable by a sequence of types in the language of C ∗ algebras. Contents