CORDIS Project
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This project explores advanced concepts in model theory and algebraic geometry, aiming to extend quantifier elimination and structural stability methods. It focuses on definable sets in global fields and their implications for number theory and geometry.
The principal methods of model theory, in its connections to algebraic geometry, have been quantifier elimination (e.g.
Tarski's theorem)and structural stability (used here in a wide sense, including simplicity, NIP and structural o-minimality.)We propose to move beyond current limitations on both fronts, by means of three interrelated projects. (1) A study of definable sets in global fields. A successful quantifier elimination result in this setting would extend the reach of model theory to…
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