3 problems

'Ez-field conjecture. All known logically tame perfect large fields, and in particular all logically tame perfect fields known before the cited work, are 'ez.

Large-field conjecture. The field ${{\mathbb Q^{\operatorname{ab}}}}$ is large.

Let $K$ be a field. Say that $K$ has almost quantifier elimination if every formula $\phi(x)$, with $x=(x_1,\ldots,x_m)$, is equivalent to a formula $\exists y\,\theta(x,y)$, where…