Modal logics of Stone spaces
type: Item
instance of: scholarly article
title: Modal logics of Stone spaces
zbMATH Open document ID: 1259.03030
author: Guram Bezhanishvili
author: John Harding
published in: Order
publication date: 2012-07-31T00:00:00Z
review text: A Stone space is an image of a Boolean algebra under Stone duality. Using their previous results, the authors characterize modal propositional logics of Stone spaces. For a metrizable Stone space \(X\) its logic is S4 if \(X\) is not weakly scattered, and is S4 or S4.\({\mathrm{Grz}_n}\) for some \(n>1\) if \(X\) is scattered. Similar results are obtained for intermediate logics.
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03B55
Mathematics Subject Classification ID: 03G05
Mathematics Subject Classification ID: 06E15
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 54G05
zbMATH DE Number: 6062530
zbMATH Keywords: modal logic
zbMATH Keywords: Boolean algebra
zbMATH Keywords: Stone space
zbMATH Keywords: metrizable space
zbMATH Keywords: extremally disconnected space
zbMATH Keywords: intuitionistic logic
zbMATH Keywords: intermediate logic
reviewed by: G. E. Mints
MaRDI profile type: Publication
full work available at URL: s11083-011-9224-2
OpenAlex ID: W2043639409
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DOI: 10.1007/S11083-011-9224-2
description: scientific article; zbMATH DE number 6062530