Post complete and 0-axiomatizable modal logics
type: Item
instance of: scholarly article
title: Post complete and 0-axiomatizable modal logics
zbMATH Open document ID: 0709.03016
DOI: 10.1016/0168-0072(90)90066-B
author: Fabio Bellissima
published in: Annals of Pure and Applied Logic
publication date: 1990-01-01T00:00:00Z
review text: A modal logic is said to be Post complete if it has no proper consistent extensions. The Post number p(L) of a logic L is the cardinal of the set of all Post complete extensions of L. The author proves that for any n, \(1\leq n\leq 2^{\aleph_ 0}\), there exist \(2^{\aleph_ 0}\) normal modal logics with Post number equal to n. The investigation is done via the study of dual spaces of free algebras without generators over the varieties of modal algebras.
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03G25
Mathematics Subject Classification ID: 08B20
zbMATH DE Number: 4164807
zbMATH Keywords: modal logic
zbMATH Keywords: Post complete
zbMATH Keywords: Post number
zbMATH Keywords: Post complete extensions
zbMATH Keywords: normal modal logics
zbMATH Keywords: free algebras
zbMATH Keywords: modal algebras
reviewed by: V. Yu. Meskhi
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4164807