# On the undecidability of infinite extensions of the rationals

## Meeting Details

Abstract: A ring $R$ is said to be decidable if there is an algorithm which decides whether arbitrary first-order formulas hold in $R$, and $R$ is undecidable otherwise. Julia Robinson proved that $\mathbb{Q}$ is undecidable, and extended this result to all finite extensions of $\mathbb{Q}$. However, the situation gets more complicated for infinite extensions of $\mathbb{Q}$. Examples show that some infinite extensions are undecidable, while others are not, and results remain unknown in general. This talk will give an overview of the known results, and present new examples of undecidable totally imaginary infinite extensions of $\mathbb{Q}$.