Some prominent conjectures in the theory of C*-algebras ask whether or not every C*-algebra of a particular form embeds into an ultrapower of a particular C*-algebra.  For example, the Kirchberg Embedding Problem asks whether every C*-algebra embeds into an ultrapower of the Cuntz algebra O_2.  In this series of lectures, we show how techniques from model theory, most notably model-theoretic forcing, can be used to give nontrivial reformulations of these conjectures.  We will start from scratch, assuming no knowledge of C*-algebras nor model theory.


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