Generalized Medvedev logics from topless finite rooted frame products are not finitely axiomatizable; at least countably many exist and none is least.
Studia Logica 75(3), pp
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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.