MacNeille completions of FL-algebras

被引：15
|
作者：
Ciabattoni, Agata [1 ]
Galatos, Nikolaos [2 ]
Terui, Kazushige [3 ]
机构：
[1] Vienna Univ Technol, Dept Comp Languages, A-1040 Vienna, Austria
[2] Univ Denver, Dept Math, Denver, CO 80208 USA
[3] Kyoto Univ, Math Sci Res Inst, Sakyo Ku, Kyoto 6068502, Japan
来源：
ALGEBRA UNIVERSALIS | 2011年 / 66卷 / 04期
基金：
奥地利科学基金会;
关键词：
Residuated lattices; completions; FL-algebras; Heyting algebras; substructural logics; superintuitionistic logics;
D O I：
10.1007/s00012-011-0160-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that a large number of equations are preserved by Dedekind-MacNeille completions when applied to subdirectly irreducible FL-algebras/residuated lattices. These equations are identified in a systematic way, based on proof-theoretic ideas and techniques in substructural logics. It follows that many varieties of Heyting algebras and FL-algebras admit completions.
引用
收藏
页码：405 / 420
页数：16
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