Roman Kossak (Bronx Community College and CUNY Graduate Center) - 
Elementary extensions - October 1, 2012

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By the Compactness Theorem, every infinite first-order structure has a proper elementary extension. This applies to infinite graphs, groups, rings, vector spaces, metric spaces, and almost anything else you can think of. Elementary extensions can be used to build interesting structures, and they can be applied to study classical structures, such as the ring of integers or the field of complex numbers, using properties of their extensions. I will explain the basic concepts and I will show some applications.
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