Provability Logics of Hierarchies

2017/04/20 by Tabatabai, Amirhossein Akbar
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1704.07678

Abstract

The branch of provability logic investigates the provability-based behavior of the mathematical theories. In a more precise way, it studies the relation between a mathematical theory T and a modal logic L via the provability interpretation which interprets the modality as the provability predicate of T. In this paper we will extend this relation to investigate the provability-based behavior of a hierarchy of theories. More precisely, using the modal language with infinitely many modalities, \\Box_n\_n=0^∞, we will define the hierarchical counterparts of some of the classical modal theories such as K4, KD4, GL and S4. Then we will define their canonical provability interpretations and their corresponding soundness-completeness theorems.

Related

• Provability Models
• Provability Interpretation of Propositional and Modal Logics
• Modal logical aspects of provability predicates and consistency statements
• The Modal Logic of Provability and Forcing
• The polytopologies of transfinite provability logic