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Preprint Number 1293
1293. Quentin Brouette, Greg Cousins, Anand Pillay, Francoise Point Embedded Picard-Vessiot extensions E-mail: Submission date: 31 August 2017 Abstract: We prove that if T is a theory of large, bounded, fields of characteristic zero, with almost quantifier elimination, and T_D is the model companion of T + “D is a derivation”, then for any model U of T_D, and differential subfield K of U whose field of constants is a model of T, and linear differential equation DY = AY over K, there is a Picard-Vessiot extension L of K for the equation which is embedded in U over K Likewise for logarithmic differential equations over K on connected algebraic groups over the constants of K and the corresponding strongly normal extensions of K. Mathematics Subject Classification: 12H05, 34M50, 03C10, 03C45 Keywords and phrases: |

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