Embedding Differential Algebraic Groups in Algebraic Groups

Quantifier Elimination We work in K a large rich differentially closed field. All other differential fields are assumed to be small subfields of K. Let L = {+,−, ·, δ, 0, 1} be the language of differential rings. We let L− = {+,−, ·, 0, 1}, the language of rings. If k is a differential field, we can view k either as an L-structure or an L−-structure. Theorem 1.1 (Quantifier Elimination) For any L-formula φ(x1, . . . , xn), there is an L-formula ψ(x1, . . . , xn) without quantifiers such that if K is a differentially closed field and a ∈ K, then