Cell Decomposition and Classification of Definable Sets in P-Optimal Fields

  title={Cell Decomposition and Classification of Definable Sets in P-Optimal Fields},
  author={Luck Darni{\`e}re and Immanuel Halupczok},
  journal={J. Symb. Log.},
  • Luck Darnière, Immanuel Halupczok
  • Published 2017
  • Mathematics, Computer Science
  • J. Symb. Log.
  • We prove that for p-optimal fields (a very large subclass of p-minimal fields containing all the known examples) a cell decomposition theorem follows from methods going back to Denef's paper [Invent. Math, 77 (1984)]. We derive from it the existence of definable Skolem functions and strong p-minimality. Then we turn to strongly p-optimal fields satisfying the Extreme Value Property (a property which in particular holds in fields which are elementarily equivalent to a p-adic one). For such… CONTINUE READING

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