Profinite Heyting algebras
type: Item
instance of: scholarly article
title: Profinite Heyting algebras
zbMATH Open document ID: 1155.06007
published in: Order
publication date: 2008-11-17T00:00:00Z
review text: A Heyting algebra \(A\) is called completely join-prime generated if every element of \(A\) is a join of completely join-prime elements of \(A\). Theorem 2.12 of this paper characterizes complete and completely join-prime generated Heyting algebras in two different ways. An algebra \(A\) is called profinite if it is isomorphic to the inverse limit of an inverse system of finite algebras. Theorem 3.6 provides five conditions, each of them characterizing profinite Heyting algebras. Several consequences of this theorem and related results are also obtained. These include Theorem 4.2, which states that the linear Heyting algebras \(L_{\infty}\) and \(L_n\) are the only profinite linear Heyting algebras, and Theorem 4.4, which characterizes profinite bounded distributive lattices.
reviewed by: Sergiu Rudeanu
Mathematics Subject Classification ID: 06D20
Mathematics Subject Classification ID: 06D50
Mathematics Subject Classification ID: 54F05
zbMATH DE Number: 5366785
zbMATH Keywords: profinite algebras
zbMATH Keywords: Heyting algebras
author: Guram Bezhanishvili
author: Nick Bezhanishvili
MaRDI profile type: Publication
full work available at URL: s11083-008-9089-1
OpenAlex ID: W2147512620
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DOI: 10.1007/S11083-008-9089-1
description: scientific article; zbMATH DE number 5366785