Undecidability, unit groups, and some totally imaginary infinite extensions of Q [article]

Caleb Springer
2020 arXiv   pre-print
We produce new examples of totally imaginary infinite extensions of Q which have undecidable first-order theory by generalizing the methods used by Martinez-Ranero, Utreras and Videla for 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. This proves the undecidability of Q^(d)_ab for all d ≥ 2.
arXiv:1910.01239v2 fatcat:v4sg5twlendnll3keyww2a2eti