Quantifier rank for parity of embedded finite models

Abstract : We prove some lower bounds for quantifier rank of formulas expressing parity of a finite set I of bounded cardinal embedded in an algebraically closed field or an ordered Q-vector space. We show that these bounds are tight when elements of I are known to be linearly independent. In the second part, we prove that strongly minimal structures with quantifier elimination and zero characteristic differentially closed fields admit the active-natural collapse.
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https://hal-lara.archives-ouvertes.fr/hal-02101892
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Submitted on : Wednesday, April 17, 2019 - 9:09:09 AM
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Hervé Fournier. Quantifier rank for parity of embedded finite models. [Research Report] LIP RR-2001-09, Laboratoire de l'informatique du parallélisme. 2001, 2+15p. ⟨hal-02101892⟩

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