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Exhibiting Wide Families of Maximal Intermediate Propositional Logics with the Disjunction Property
Author(s) -
Bertolotti Guido,
Miglioli Pierangelo,
Silvestrini Daniela
Publication year - 1996
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19960420141
Subject(s) - mathematics , propositional variable , axiom , cardinality (data modeling) , property (philosophy) , kripke semantics , propositional formula , monoidal t norm logic , propositional calculus , axiom of choice , discrete mathematics , set (abstract data type) , intermediate logic , set theory , computer science , theoretical computer science , epistemology , artificial intelligence , philosophy , programming language , description logic , geometry , fuzzy number , fuzzy set , data mining , fuzzy logic
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 2 No 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.