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
相关论文
共 19 条
  • [1] MacNeille completions of FL-algebras
    Agata Ciabattoni
    Nikolaos Galatos
    Kazushige Terui
    Algebra universalis, 2011, 66 : 405 - 420
  • [2] Relation algebras as expanded FL-algebras
    Galatos, Nikolaos
    Jipsen, Peter
    ALGEBRA UNIVERSALIS, 2013, 69 (01) : 1 - 21
  • [3] Complemented MacNeille completions and algebras of fractions
    Galatos, Nick
    Prenosil, Adam
    JOURNAL OF ALGEBRA, 2023, 623 : 288 - 357
  • [4] Hyper-MacNeille Completions of Heyting Algebras
    J. Harding
    F. M. Lauridsen
    Studia Logica, 2021, 109 : 1119 - 1157
  • [5] Hyper-MacNeille Completions of Heyting Algebras
    Harding, J.
    Lauridsen, F. M.
    STUDIA LOGICA, 2021, 109 (05) : 1119 - 1157
  • [6] MacNeille completions of lattice expansions
    Theunissen, Mark
    Venema, Yde
    ALGEBRA UNIVERSALIS, 2007, 57 (02) : 143 - 193
  • [7] MacNeille completions of lattice expansions
    Mark Theunissen
    Yde Venema
    Algebra universalis, 2007, 57 : 143 - 193
  • [8] Completions of μ-algebras
    Santocanale, Luigi
    ANNALS OF PURE AND APPLIED LOGIC, 2008, 154 (01) : 27 - 50
  • [9] Supersound many-valued logics and Dedekind-MacNeille completions
    Bianchi, Matteo
    Montagna, Franco
    ARCHIVE FOR MATHEMATICAL LOGIC, 2009, 48 (08): : 719 - 736
  • [10] MacNeille transferability and stable classes of Heyting algebras
    Bezhanishvili, Guram
    Harding, John
    Ilin, Julia
    Lauridsen, Frederik Mollerstrom
    ALGEBRA UNIVERSALIS, 2018, 79 (03)
12