Noetherian varieties in definably complete structures

@article{Servi2008NoetherianVI,
  title={Noetherian varieties in definably complete structures},
  author={Tamara Servi},
  journal={Logic and Analysis},
  year={2008},
  volume={1},
  pages={187-204}
}
  • Tamara Servi
  • Published 2008
  • Mathematics, Computer Science
  • Logic and Analysis
We prove that the zero-set of a C∞ function belonging to a noetherian differential ring M can be written as a finite union of C∞ manifolds which are definable by functions from the same ring. These manifolds can be taken to be connected under the additional assumption that every zero-dimensional regular zero-set of functions in M consists of finitely many points. These results hold not only for C∞ functions over the reals, but more generally for definable C∞ functions in a definably complete… Expand
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