Grzegorczyk Logic Unlocked
Logic
2026-02-17 v2
Abstract
The article offers a fresh perspective on Grzegorczyk logic Grz, introducing a simplified axiomatization and extending the analysis to its natural modal extensions, Grz.2 and Grz.3. I develop a control statement theory for these logics, utilizing concepts such as buttons, switches, and ratchets. Through this framework, I establish that Grz.2 is characterized by finite Boolean algebras.
Keywords
Cite
@article{arxiv.2505.09836,
title = {Grzegorczyk Logic Unlocked},
author = {Wojciech Aleksander Wołoszyn},
journal= {arXiv preprint arXiv:2505.09836},
year = {2026}
}