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A Proof Theory for Profinite Modal Algebras
Matteo De Berardinis, Silvio Ghilardi
https://arxiv.org/abs/2507.06007 https://arxiv.org/…

A Proof Theory for Profinite Modal Algebras
In a previous paper, we showed that profinite $L$-algebras (where $L$ is a variety of modal algebras generated by its finite members) are monadic over $\mathbf{Set}$. This monadicity result suggests that profinite $L$-algebras could be presented as Lindenbaum algebras for propositional theories in infinitary versions of propositional modal calculi. In this paper we identify such calculi as modal enrichments of Maehara-Takeuti's infinitary extension of the sequent calculus $\mathbf{LK}$. We also…