abstract
Section 1 contains a Kripke-style completeness theorem for arbitrary intermediate consequences. In Section 2 we apply weak Kripke semantics to splittings in order to obtain generalized axiomatization criteria of the Jankov-type. Section 3 presents new and short proofs of recent results on implicationless intermediate consequences. In Section 4 we prove that these consequences admit no deduction theorem. In Section 5 all maximal logics in the 3rd counterslice are determined. On these results we reported at the 1980 meeting on Mathematical Logic at Oberwolfach. This paper concerns propositional logic only.
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Rautenberg, W. Applications of weak Kripke semantics to intermediate consequences. Stud Logica 45, 119–134 (1986). https://doi.org/10.1007/BF01881553
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DOI: https://doi.org/10.1007/BF01881553