On the decidability of the field of maximal abelian extension of p-adic numbers

On the decidability of the field of maximal abelian extension of p-adic numbers

<p>In this project we investigate some approaches attacking the question of whether the theory of the maximal abelian extension of the p-adic numbers is decidable. A list of axioms is presented whose completeness we aim to show via quantifier elimination. We separated the quantifier eliminatio...

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Detalhes bibliográficos
Autor principal: Wang, C
Outros Autores: Koenigsmann, J
Formato: Tese
Publicado em: 2018
Descrição
Resumo:<p>In this project we investigate some approaches attacking the question of whether the theory of the maximal abelian extension of the p-adic numbers is decidable. A list of axioms is presented whose completeness we aim to show via quantifier elimination. We separated the quantifier elimination process into five embedding stages. We constructed four of the embeddings, up to the subextension field whose residue field is algebraically closed. For the last stage, some possible approaches are discussed.</p>

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