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1 results

  • THE FIELD OF p-ADIC NUMBERS WITH A PREDICATE FOR THE POWERS OF AN INTEGER

  • NATHANAËL MARIAULE
  • Journal:
    The Journal of Symbolic Logic / Volume 82 / Issue 1 / March 2017
    Published online by Cambridge University Press:
    21 March 2017, pp. 166-182
    Print publication:
    March 2017

  • In this paper, we prove the decidability of the theory of ℚp in the language (+, −,⋅, 0, 1, Pn(n ∈ ℕ)) expanded by a predicate for the multiplicative subgroup nℤ (where n is a fixed integer). There are two cases: if $v_p \left( n \right) > 0$ then the group determines a cross-section and we get an axiomatization of the theory and a result of quantifier elimination. If $v_p \left( n \right) = 0$, then we use the Mann property of the group to get an axiomatization of the theory.