The Algebra Seminar series presents Shehzad Ahmed of Ohio University discussing “Applications of Model Theory to Algebra” on Wednesday, April 20, at 4 p.m. in Morton 318.
Abstract: This talk is a continuation of the most recent talk I gave on Model Theory. Now that we have laid down the model-theoretic foundations, my goal is to give an idea of how this machinery is used in algebra. Our attention will be focused on the theories of algebraically closed fields and real closed fields, and we will take for granted that both theories admit quantifier elimination. Using this, we will give model theoretic proofs of Hilbert’s Nullstellensatz, as well as the Tarski-Siedenberg theorem regarding semi-algebraic sets subsets of R^n. Time permitting, we will discuss other tools and their applications such as ultraproducts and the Lowenheim-Skolem theorems.
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