Quantifier rank for parity of embedded finite models

(eng) 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

Quantifier rank for parity of embedded finite models

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.On prouve des bornes inférieures pour le rang de quantification de formules exprimant la parité d'un ensemble fini I de cardinal borné, plongé dans un corps algébriquement clos ou un Q-espace vectoriel ordonnée. De plus, ces bornes se trouvent être précises dans le cas où on impose aux éléments de I d'être linéairement indépendants. Dans la seconde partie, on montre que les structures fortement minimales éliminant les quantificateurs et les corps différentiellement clos de caractéristique nulle admettent le collapse actif-nature

Quantifier rank for parity of embedded finite models

SIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : RP 15831 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc