On Algebraic Curves over Real Closed Fields. II.
Manfred Knebusch (1976)
Mathematische Zeitschrift
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Manfred Knebusch (1976)
Mathematische Zeitschrift
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Manfred Knebusch (1976)
Mathematische Zeitschrift
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E. Bujalance, J.J. Etayo, J.M. Gamboa (1987)
Mathematische Zeitschrift
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Allen Tannenbaum (1980)
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Gerard van der Geer, M. van der Vlugt (1992)
Mathematische Zeitschrift
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Manfred Knebusch (1977)
Mathematische Zeitschrift
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Jyotsna Gokhale (1994)
Mathematische Zeitschrift
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Trygve Johnsen (1992)
Mathematische Zeitschrift
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L.S. Hulburt (1891/92)
Bulletin of the New York Mathematical Society
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B. L. Moore (1922)
Mathematische Zeitschrift
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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...
Schröder (1876)
Mathematische Annalen
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A. Dolcetti, G. Pareschi (1988)
Mathematische Zeitschrift
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Sheng-Li Tan (1996)
Mathematische Zeitschrift
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