6 problems

Pretransitivity conjecture. If a normal modal logic $\Lambda$ is interpretable by a modal-to-modal translation with parameters in a pretransitive normal logic, then $\Lambda$ is pr…

Let $A$ be a finitely axiomatized Vaught theory in signature $\Theta_0$, let $N:A\rhd{\sf R}$, and suppose $\top\rhd_A{\sf TB}^{-}_N$. Finite-approximation conjecture. There is a…

Let $U$ be a Vaught theory and let $N:{\sf R}\lhd U$. For theories or axiom sets $\alpha$ and $\Gamma$, write \alpha\mathrel{\text{\textcolor{gray}{blacktriangleright…

Let $A$ be finitely axiomatized, consistent, and sequential, and let $N:{\sf S}^1_2\lhd A$. Write $A+{\sf TB}^{-}_N$ for the corresponding Tarski-biconditional extension. Mutual-in…

Let $U$ be a Vaught theory, meaning a theory with the relevant direct interpretation properties described in the paper. Call $U$ Enayat when it interprets itself together with the…

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 c…