5 problems

Let $T_{\rm fg}$ denote the first-order theory of nonabelian free groups. An infinite field is interpretable in $T_{\rm fg}$ if its underlying set, operations, and relations can be…

Let $\mathbb T$ be the differential field of logarithmic-exponential transseries, and let $\mathbb R$ be the real field. Write $\mathbb T[\imag]$ and $\mathbb C=\mathbb R[\imag]$ f…

Definable-isomorphism conjecture. Any infinite field interpretable in $K$ is $K$-definably isomorphic to some finite extension of $K$.

Let $G$ be a torsion-free hyperbolic group, and let $\mathcal{M}$ be a model of $Th(G)$. An interpretable group is a group interpretable in $\mathcal{M}$. Definable-embedding conje…

Let $G$ be a torsion-free hyperbolic group. An interpretable field is a field interpretable in a model of $Th(G)$. No-interpretable-fields conjecture. No infinite field is interpre…