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An infinite class of maximal intermediate propositional logics with the disjunction property

Pierangelo Miglioli

Archive for Mathematical Logic 31 (6):415-432 (1992)

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On maximal intermediate predicate constructive logics.Alessandro Avellone, Camillo Fiorentini, Paolo Mantovani & Pierangelo Miglioli - 1996 - Studia Logica 57 (2-3):373 - 408.details We extend to the predicate frame a previous characterization of the maximal intermediate propositional constructive logics. This provides a technique to get maximal intermediate predicate constructive logics starting from suitable sets of classically valid predicate formulae we call maximal nonstandard predicate constructive logics. As an example of this technique, we exhibit two maximal intermediate predicate constructive logics, yet leaving open the problem of stating whether the two logics are distinct. Further properties of these logics will be also investigated. Download Export citation Bookmark 1 citation
Preface. In memoriam Pierangelo Miglioli (1946–1999).Mario Ornaghi - 2003 - Studia Logica 73 (1):5-19.details Download Export citation Bookmark
Counting the maximal intermediate constructive logics.Mauro Ferrari & Pierangelo Miglioli - 1993 - Journal of Symbolic Logic 58 (4):1365-1401.details A proof is given that the set of maximal intermediate propositional logics with the disjunction property and the set of maximal intermediate predicate logics with the disjunction property and the explicit definability property have the power of continuum. To prove our results, we introduce various notions which might be interesting by themselves. In particular, we illustrate a method to generate wide sets of pairwise "constructively incompatible constructive logics". We use a notion of "semiconstructive" logic and define wide sets of "constructive" (...) Download Export citation Bookmark 6 citations
A method to single out maximal propositional logics with the disjunction property I.Mauro Ferrari & Pierangelo Miglioli - 1995 - Annals of Pure and Applied Logic 76 (1):1-46.details This is the first part of a paper concerning intermediate propositional logics with the disjunction property which cannot be properly extended into logics of the same kind, and are therefore called maximal. To deal with these logics, we use a method based on the search of suitable nonstandard logics, which has an heuristic content and has allowed us to discover a wide family of logics, as well as to get their maximality proofs in a uniform way. The present part illustrates (...) Download Export citation Bookmark 3 citations
A method to single out maximal propositional logics with the disjunction property II.Mauro Ferrari & Pierangelo Miglioli - 1995 - Annals of Pure and Applied Logic 76 (2):117-168.details This is the second part of a paper devoted to the study of the maximal intermediate propositional logics with the disjunction property , whose first part has appeared in this journal with the title “A method to single out maximal propositional logics with the disjunction property I”. In the first part we have explained the general results upon which a method to single out maximal constructive logics is based and have illustrated such a method by exhibiting the Kripke semantics of (...) Download Export citation Bookmark 5 citations

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