Relational Semantics for the Turing Schmerl Calculus
Eduardo Hermo Reyes, Joost J. Joosten · arXiv (Cornell University) · 2017
In arXiv:1604.08705 the authors introduced the propositional modal logic $\textbf{TSC}$ (which stands for Turing Schmerl Calculus) which adequately describes the provable interrelations between different kinds of Turing progressions. The current paper defines a model $\mathcal{J}$ which is proven to be a universal model for $\textbf{TSC}$. The model $\mathcal{J}$ is a slight modification of the intensively studied $\mathcal{I}$ : Ignatiev's universal model for the closed fragment of Gödel Löb's polymodal provability logic $\textbf{GLP}$.