• Corpus ID: 224714585

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

@article{Eisentrger2020ATA,
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},
year={2020}
}
• Published 19 October 2020
• Mathematics
• 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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