Model Theory for Algebraic Geometry
نویسنده
چکیده
We demonstrate how several problems of algebraic geometry, i.e. Ax-Grothendieck, Hilbert’s Nullstellensatz, NoetherOstrowski, and Hilbert’s 17th problem, have simple proofs when approached from using model theory. The proofs use two general transfer principles. The first is the Lefschetz principle, which allows sentences that are true in algebraically closed fields of infinitely many prime characteristics to transfer to algebraically closed fields of characteristic 0. The second is model completeness, which allows sentences that are true in an algebraically closed field or real closed field to transfer down to an algebraically closed subfield or real closed subfield, respectively.
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