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We show that for for k ≥ 6, the class S 𝔑𝔯 3 CA k is not closed under completions and is not Sahlqvist axiomatizable. This generalizes results in (3) and (5) for RCA n when n=3. 1
After some motivating remarks in Section 1, in Section 2 we show how to replace an axiomatic basis for any one of a broad range of sentential logics having finitely many axiom schemes and Modus Ponens as the sole proper rule, by a basis with the same axiom schemes and finitely many one-premiss...
Hereditary structural completeness is established for a range of substructural logics, mainly without the weakening rule, including fragments of various relevant or many-valued logics. Also, structural completeness is disproved for a range of systems, settling some previously open questions.
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