Undecidability, unit groups, and some totally imaginary infinite extensions of $\mathbb{Q}$
| Autor: | Springer, Caleb |
|---|---|
| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. This proves the undecidability of $\mathbb{Q}^{(d)}_{ab}$ for all $d \geq 2$. Comment: 11 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|