Small inductive dimension and universality on frames

被引:0
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作者
Dimitrios N. Georgiou
Stavros D. Iliadis
Athanasios C. Megaritis
Fotini Sereti
机构
[1] University of Patras,Department of Mathematics
[2] Moscow State University (M. V. Lomonosov),Department of General Topology and Geometry
[3] Technological Educational Institute of Peloponnese,Department of Computer Engineering
来源
Algebra universalis | 2019年 / 80卷
关键词
Small inductive dimension of frames; Universal frame; Saturated class of frames; 06A06; 06D22; 06F30; 54H12; 54F05;
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摘要
In this paper we prove that for a fixed integer or an ordinal α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} and a fixed infinite cardinal τ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau $$\end{document} the class of all regular frames of weight less than or equal to τ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau $$\end{document} with small inductive dimension less than or equal to α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} is saturated and therefore, in this class of frames there exist universal elements.
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