Speaker: Alexey Muranov Title: Interpretability of the Arithmetic in certain finitely presented groups. A recent article on \texttt{arXiv.org} of Bardakov and Tolstykh shows that the Arithmetic is interpretable with parameters in Thompson's group $F$. This group $F$ is finitely presented, and is usually regarded as a subgroup of two other groups of Thompson, $T$ and $V$, which are simple and finitely presented as well. The group $V$ is also a member of a series of simple finitely presented groups described by Higman in 1974. We have extended the result of Bardakov and Tolstykh by interpreting the Arithmetic in all the groups of Thompson and Higman, and have considered some other first-order properties of such groups. In my talk, I shall present our results and questions on this subject.