• Corpus ID: 224714585

A topological approach to undefinability in algebraic extensions of $\mathbb{Q}$.

  title={A topological approach to undefinability in algebraic extensions of \$\mathbb\{Q\}\$.},
  author={Kirsten Eisentr{\"a}ger and Russell G. Miller and Caleb Springer and Linda Brown Westrick},
  journal={arXiv: Number Theory},
In this paper we investigate the algebraic extensions $K$ of $\mathbb{Q}$ in which we cannot existentially or universally define the ring of integers $\mathcal{O}_K$. A complete answer to this question would have important consequences. For example, the existence of an existential definition of $\mathbb{Z}$ in $\mathbb{Q}$ would imply that Hilbert's Tenth Problem for $\mathbb{Q}$ is undecidable, resolving one of the biggest open problems in the area. However, a conjecture of Mazur implies that… 


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