Grzegorczyk Logic Unlocked

2025/05/14 by Wojciech Aleksander Wołoszyn, Wołoszyn, Wojciech Aleksander
Mathematics · #History and Theory of Mathematics

paper · pdf · doi:10.48550/arxiv.2505.09836

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.

Citations

• The modal logic of arithmetic potentialism and the universal algorithm
• The universal finite set
• The modal logic of set-theoretic potentialism and the potentialist\n maximality principles
• Structural connections between a forcing class and its modal logic
• The modal logic of forcing

Related

• Non-Well-Founded Proofs for the Grzegorczyk Modal Logic
• The Monadic Grzegorczyk Logic
• Cut-elimination for the modal Grzegorczyk logic via non-well-founded proofs
• Cut Elimination for Weak Modal Grzegorczyk Logic via Non-Well-Founded Proofs
• Some modal and temporal translations of generalized basic logic