Generalized Medvedev logics from topless finite rooted frame products are not finitely axiomatizable; at least countably many exist and none is least.
Jankov Formulas and Axiomatization Techniques for Intermediate Logics
2 Pith papers cite this work. Polarity classification is still indexing.
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The Subdivision Construction produces finite modal algebras as countermodels for stable canonical rules of finite height, establishing the finite model property for broad classes of modal logics and rule systems.
citing papers explorer
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Non-finite Axiomatizability of Generalized Medvedev Logics
Generalized Medvedev logics from topless finite rooted frame products are not finitely axiomatizable; at least countably many exist and none is least.
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Chopping More Finely: Finite Countermodels in Modal Logic via the Subdivision Construction
The Subdivision Construction produces finite modal algebras as countermodels for stable canonical rules of finite height, establishing the finite model property for broad classes of modal logics and rule systems.