Relational Semantics for the Turing Schmerl Calculus

Abstract

In arXiv:1604.08705 the authors introduced the propositional modal logic $\text{TSC}$ (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 $\text{TSC}$. 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 $\text{GLP}$.

Cited by in corpus (2)

• The logic of Turing progressions
• A Finitely Supported Frame for the Turing Schmerl Calculus