Real Algebraic Curves as Complete Intersections.
Wojciech Kucharz (1987)
Mathematische Zeitschrift
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Wojciech Kucharz (1987)
Mathematische Zeitschrift
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Eldon Jon Vought (1969)
Colloquium Mathematicae
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Serge Randriambololona, Sergei Starchenko (2011)
Fundamenta Mathematicae
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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...
E. Bujalance, J.J. Etayo, J.M. Gamboa (1987)
Mathematische Zeitschrift
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A. Lelek (1971)
Colloquium Mathematicae
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Slavik Jablan (2001)
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Nat Friedman (2001)
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Balan, Vladimir (2003)
Balkan Journal of Geometry and its Applications (BJGA)
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Paulus Gerdes (2002)
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Mark D. Schlatter (2005)
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Mošová, Vratislava
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