# Undecidability, unit groups, and some totally imaginary infinite extensions of \$\mathbb{Q}\$

31 May 2020 Springer Caleb

We produce new examples of totally imaginary infinite extensions of \$\mathbb{Q}\$ which have undecidable first-order theory by generalizing the methods used by Martinez-Ranero, Utreras and Videla for \$\mathbb{Q}^{(2)}\$. In particular, we use parametrized families of polynomials whose roots are totally real units to apply methods originally developed to prove the undecidability of totally real fields... (read more)

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• NUMBER THEORY
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