G R ] 3 0 D ec 2 00 3 1 Implicit function theorem over free groups

@inproceedings{Kharlampovich2009GR,
  title={G R ] 3 0 D ec 2 00 3 1 Implicit function theorem over free groups},
  author={Olga Kharlampovich and A. D. Myasnikov},
  year={2009}
}
We introduce the notion of a regular quadratic equation and a regular NTQ system over a free group. We prove the results that can be described as Implicit function theorems for algebraic varieties corresponding to regular quadratic and NTQ systems. We will also show that the Implicit function theorem is true only for these varieties. In algebraic geometry such results would be described as lifting solutions of equations into generic points. From the model theoretic view-point we claim the… CONTINUE READING
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