We prove that if T is a theory of large, bounded, fields of characteristic 0 with almost quantifier elimination, and T-D is the model companion of T{ is a derivation}, then for any model (?,) of T-D, differential subfield K of ? such that C-K?T, and linear differential equation Y=AY over K, there is a Picard-Vessiot extension L of K for the equation with KL?, i.e. L can be embedded in ? over K, as a differential field. Moreover such L is unique to isomorphism over K as a differential field. Likewise for the analogue for strongly normal extensions for logarithmic differential equations in the sense of Kolchin.
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