Grzegorczyk Logic Unlocked
Wojciech Aleksander Wołoszyn
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.