The conjecture that no finitely axiomatized consistent sequential theory is Enayat

Let $U$ be a sequential theory. It is Enayat when it interprets itself together with the Tarski biconditionals for its language. Sequential Enayat-theory conjecture. There are no consistent, finitely axiomatized, sequential Enayat theories. This is the central open problem motivating the paper and is presented as the sequential form of Enayat's question.