Some (non-)elimination results for curves in geometric structures

• Autorzy: Serge Randriambololona , Sergei Starchenko
• Języki publikacji: EN

Abstrakty

EN

We show that the first order structure whose underlying universe is ℂ and whose basic relations are all algebraic subsets of ℂ² does not have quantifier elimination. Since an algebraic subset of ℂ² is either of dimension ≤ 1 or has a complement of dimension ≤ 1, one can restate the former result as a failure of quantifier elimination for planar complex algebraic curves. We then prove that removing the planarity hypothesis suffices to recover quantifier elimination: the structure with the universe ℂ and a predicate for each algebraic subset of ℂⁿ of dimension ≤ 1 has quantifier elimination.

Kategorie tematyczne

• 03C60: Model-theoretic algebra
• 03C10: Quantifier elimination, model completeness and related topics
• 14H50: Plane and space curves

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 214
• Numer: 2
• Strony: 181-198

Daty

wydano

2011

Twórcy

autor

Serge Randriambololona

• Department of Mathematics, The University of Western Ontario, London, Ontario N6A 5B7, Canada

autor

Sergei Starchenko

• Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, U.S.A.

Identyfikatory

DOI

10.4064/fm214-2-5