Uniformly defining p-henselian valuations

@article{Jahnke2015UniformlyDP,
  title={Uniformly defining p-henselian valuations},
  author={F. Jahnke and J. Koenigsmann},
  journal={Ann. Pure Appl. Log.},
  year={2015},
  volume={166},
  pages={741-754}
}
  • F. Jahnke, J. Koenigsmann
  • Published 2015
  • Mathematics, Computer Science
  • Ann. Pure Appl. Log.
  • Admitting a non-trivial $p$-henselian valuation is a weaker assumption on a field than admitting a non-trivial henselian valuation. Unlike henselianity, $p$-henselianity is an elementary property in the language of rings. We are interested in the question when a field admits a non-trivial 0-definable $p$-henselian valuation (in the language of rings). We give a classification of elementary classes of fields in which the canonical $p$-henselian valuation is uniformly 0-definable. We then apply… CONTINUE READING

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