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

页码：405 / 420

页数：16

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