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In this paper, we prove the decidability of the theory of ℚ p in the language (+, −,⋅, 0, 1, P n (n ∈ ℕ)) expanded by a predicate for the multiplicative subgroup n (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.



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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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