Continuality of the set of maximal superintuitionistic logics with the disjunction property
type: Item
instance of: scholarly article
title: Continuality of the set of maximal superintuitionistic logics with the disjunction property
zbMATH Open document ID: 0795.03030
DOI: 10.1007/BF02102127
published in: Mathematical Notes
publication date: 1994-02-08T00:00:00Z
review text: A superintuitionistic logic is a logic containing intuitionistic logic. Here the author treats only consistent superintuitionistic propositional logics, that is, the intermediate propositional logics. The disjunction property for a logic says that if ``\(A\) or \(B\)'' belongs to the logic, then either \(A\) or \(B\) belongs to it. In this paper, the cardinality of the maximal intermediate logics with the disjunction property is studied and as the Main Theorem, it is proved that there are a continuum of such maximal logics. Besides the Main Theorem, this note presents good information around the problem.
Mathematics Subject Classification ID: 03B55
zbMATH DE Number: 484247
zbMATH Keywords: superintuitionistic logic
zbMATH Keywords: intermediate propositional logics
zbMATH Keywords: cardinality of the maximal intermediate logics with the disjunction property
author: Alexander Vasil'evich Chagrov
reviewed by: Tsutomu Hosoi
MaRDI profile type: Publication
cites work: Q4065518
cites work: On maximal intermediate logics with the disjunction property
cites work: Q3783273
cites work: Intermediate logics with the same disjunctionless fragment as intuitionistic logic
description: scientific article; zbMATH DE number 484247