THE FIELD OF p-ADIC NUMBERS WITH A PREDICATE FOR THE POWERS OF AN INTEGER
| Autor: | Nathanaël Mariaule |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Logic 010102 general mathematics 0102 computer and information sciences Predicate (mathematical logic) 01 natural sciences Trial division Combinatorics Philosophy 010201 computation theory & mathematics Prime factor ComputingMethodologies_DOCUMENTANDTEXTPROCESSING 0101 mathematics Radical of an integer Smooth number Mathematics p-adic number |
| Zdroj: | The Journal of Symbolic Logic. 82:166-182 |
| ISSN: | 1943-5886 0022-4812 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|