Some compactness results for modal logic
type: Item
instance of: scholarly article
title: Some compactness results for modal logic
zbMATH Open document ID: 0682.03010
author: George F. Schumm
published in: Notre Dame Journal of Formal Logic
publication date: 1989-01-01T00:00:00Z
review text: A modal logic L is compact iff every L-consistent set of wff can be simultaneously satisfied at some point in a frame for L. L is canonical iff every theorem of L is valid on the frame of the canonical model of L. It is trivial that if L is canonical then L is compact. It is not known whether the converse holds. The author proves that the converse does hold for any logics whose frames contain no worlds with infinitely many alternatives. He then widens one of the classes of logics for which non- compactness is known, and another class of logics for which canonicity, and therefore compactness is known. He finally uses results obtained elsewhere to show that there are uncountably many canonical logics and uncountably many non compact extensions of S4 with the finite model property.
Mathematics Subject Classification ID: 03B45
zbMATH DE Number: 4116500
zbMATH Keywords: modal logic
zbMATH Keywords: compactness
reviewed by: M. J. Cresswell
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1093635085
OpenAlex ID: W1998911560
DOI: 10.1305/NDJFL/1093635085
description: scientific article; zbMATH DE number 4116500