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

Caleb Springer

Published 2019-10-02Version 1

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.