Exhibiting Wide Families of Maximal Intermediate Propositional Logics with the Disjunction Property

• Published in: Mathematical logic quarterly Vol. 42; no. 1; pp. 501 - 536
• Main Authors: Bertolotti, Guido, Miglioli, Pierangelo, Silvestrini, Daniela
• Format: Journal Article
• Language: English
• Published: Berlin WILEY-VCH Verlag Berlin GmbH 1996; WILEY‐VCH Verlag Berlin GmbH
• Subjects: Constructive logic; Intermediate logic; Irreductible frame; Kripke frame semantics; Kripke model; Maximal constructive logic; Maximal nonstandard constructive logic; Nonstandard constructive logic; Nonstandard intermediate logic; Regular Kripke model; Weak canonical model
• ISSN: 0942-5616; 1521-3870
• DOI: 10.1002/malq.19960420141

We provide results allowing to state, by the simple inspection of suitable classes of posets (propositional Kripke frames), that the corresponding intermediate propositional logics are maximal among the ones which satisfy the disjunction property. Starting from these results, we directly exhibit, without using the axiom of choice, the Kripke frames semantics of 2No maximal intermediate propositional logics with the disjunction property. This improves previous evaluations, giving rise to the same conclusion but made with an essential use of the axiom of choice, of the cardinality of the set of the maximal intermediate propositional logics with the disjunction property. Mathematics Subject Classification: 03B55, 03C90.