Model theory and operator algebras

模型论是数理逻辑的一个分支，它成功地为其他数学分支的问题提供了新的解决方案。 一般来说，要从理论上研究一个数学对象模型，人们考虑的不是所讨论的对象，而是用适当选择的语言研究对象的理论。 通过研究这个理论的所有模型，有时可以得出关于原始结构的结论。 最近，随着连续模型理论的发展，应用到某些分支的分析，以前是遥不可及的模型理论已变得更加听话。 在这个建议中，我建议一个系统的模型理论研究算子代数的基础上，最近成功的工作，我自己和合著者在解决问题的可分代数的超幂。 似乎有有趣的可能性，模型理论可以提供援助的问题有关的问题冯诺依曼代数和一个关键类的C*-代数，如核C*-代数。 短期目标是扩大对应用领域模型理论方法的理解，但从长远来看，随着对这两个领域技术的更好理解，将有可能在加拿大两个强大的研究社区的边界上证明重大成果。

Model theory is a branch of mathematical logic which has had success in providing novel attacks on problems in other branches of mathematics. Generally speaking, to study a mathematical object model theoretically, one considers not the object in question but the theory of the object in a suitably chosen language. By studying all the models of this theory, it is sometimes possible to draw conclusions about the original structure. Recently, with the development of continuous model theory, applications to certain branches of analysis which were previously out of reach for model theory have become more tractable. In this proposal, I suggest a systematic model theoretic study of operator algebras based on recent success of work of myself and co-authors in settling questions related to ultrapowers of separable algebras. There seems to be the intriguing possibility that model theory can provide assistance with problems related to questions about von Neumann algebras and a critical classes of C*-algebras such as nuclear C*-algebras. The short term objective is to widen the understanding of model theoretic methods in application areas but in the long run, with a better understanding of the techniques from both fields, it will be possible to prove significant results on the borders of two of Canada's strong research communities.