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Model Theory and Exponentiation

Lunedi 7 giugno - prof. David Marker

ARGOMENTI: Seminari

Lunedi 7 giugno, alle ore 16:30 in aula 2AB/45 il prof. David Marker (UIC Chicago) terra' un seminario dal titolo "Model Theory and Exponentiation".

-Abstract
Model theory, a branch of mathematical logic, has in recent years, had surprising applications to classical mathematical questions.
This can be traced back to Tarski who showed that--in stark contrast to Godel's results about the integers--there is an algorithm to decide the theory of the real numbers. Tarski's method has become a powerful tool in real algebraic and semialgebraic geometry to show that definable sets have very nice geometric and topological properties. Model theoretic methods have been very useful in extending these ideas when the real field is equipped with extra structure. In particular, Wilkie showed that these properties are shared by sets definable in the real field with exponentiation. In contrast, when one looks at the complex field with exponentiation, one can easily define the integers, so one is subject to all of the Godel phenomena. Nevertheless, Zilber has proposed a model theoretic approach that might salvage some structure theory and leads to a fascinating series of questions about complex exponentiation.

Rif. int. M. A. Garuti

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