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Model Theory, as a subject, has grown tremendously over the last few
decades. Starting out as a branch of mathematical logic, it has now wide
applications in most branches of mathematics, with algebra, algebraic
geometry, number theory, combinatorics and even analysis to name a few. In
this talk, I will give a brief introduction to model theory, talk about
the compactness theorem (one of the main tools in model theory) and how it
is used, and give one famous application of model theory to algebra,
namely, the Ax-Kochen Theorem, the answer to Artin's Conjecture. Time
permitting, I will talk about a few more recent results in this direction.
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