Relational Semantics for the Turing Schmerl Calculus

2017/09/14 by Eduardo Hermo Reyes, Joost J. Joosten, Reyes, Eduardo Hermo +1
Computer Science · #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Semantic Web and Ontologies

paper · pdf · doi:10.48550/arxiv.1709.04715

openalex publication_date 2017/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In arXiv:1604.08705 the authors introduced the propositional modal logic 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 J which is proven to be a universal model for TSC. The model J is a slight modification of the intensively studied I : Ignatiev's universal model for the closed fragment of Gödel Löb's polymodal provability logic GLP.

Related

• A Finitely Supported Frame for the Turing Schmerl Calculus
• Models of transfinite provability logic
• The polytopologies of transfinite provability logic
• Proof systems: from nestings to sequents and back
• Well-orders in the transfinite Japaridze algebra II: Turing progressions and their well-orders