Decidable theories of non-projectable \(l\)-groups of continuous functions
type: Item
instance of: scholarly article
title: Decidable theories of non-projectable \(l\)-groups of continuous functions
zbMATH Open document ID: 1115.06012
author: Brian Wynne
published in: Annals of Pure and Applied Logic
publication date: 2007-04-18T00:00:00Z
review text: An (abelian) \(\ell \)-group \(G\) is called projectable if for every \(0<a\in G\) the interval \([0,a]\) is pseudocomplemented. If \(X\) is a topological space then \(C(X)\) denotes the \(\ell \)-group of all continuous real-valued functions on \(X\). The author studies the class of \(\ell \)-groups \(C(X)\) such that \(X\) is a so-called essential \(P\)-space. In the paper it is shown that many of such \(\ell \)-groups are non-projectable and that their elementary theories may often be reduced to those of associated Boolean algebras with distinguished ideals. This is used to establish the decidability of two classes of \(\ell \)-groups of continuous functions which, among others, are not projectable.
Mathematics Subject Classification ID: 06F20
Mathematics Subject Classification ID: 03B25
Mathematics Subject Classification ID: 54C30
zbMATH DE Number: 5144414
zbMATH Keywords: \(l\)-group
zbMATH Keywords: decidable theory
zbMATH Keywords: \(P\)-space
zbMATH Keywords: Boolean algebra
reviewed by: Jiří Rachůnek
MaRDI profile type: Publication
full work available at URL: j.apal.2006.12.002
OpenAlex ID: W2089255079
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DOI: 10.1016/J.APAL.2006.12.002
description: scientific article; zbMATH DE number 5144414