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Creators/Authors contains: "Jaoui, Rémi"

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  1. ; ; (, Journal of Mathematical Logic)
    In this paper, it is shown that if p is a complete type of Lascar rank at least 2, in the theory of differentially closed fields of characteristic zero, then there exists a pair of realisations a, b such that p has a nonalgebraic forking extension over a, b. Moreover, if A is contained in the field of constants then p already has a nonalgebraic forking extension over a. The results are also formulated in a more general setting. 
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  2. ; ; (, Inventiones mathematicae)
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  3. ; ; ; (, International Mathematics Research Notices)
    Abstract We study the structure of the solution sets in universal differential fields of certain differential equations of order two, the Poizat equations, which are particular cases of Liénard equations. We give a necessary and sufficient condition for strong minimality for equations in this class and a complete classification of the algebraic relations for solutions of strongly minimal Poizat equations. We also give an analysis of the non-strongly minimal cases as well as applications concerning the Liouvillian and Pfaffian solutions of some Liénard equations. 
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