Unilinear residuated lattices: axiomatization, varieties and FEP

被引：0
|
作者：
Galatos, Nikolaos [1 ]
Zhuang, Xiao [1 ]
机构：
[1] Univ Denver, Dept Math, Denver, CO 80208 USA
来源：
ALGEBRA UNIVERSALIS | 2024年 / 85卷 / 03期
关键词：
Unilinear residuated lattices; Axiomatization; Subvarieties; Finite embeddability property; FINITENESS;
D O I：
10.1007/s00012-024-00856-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We characterize all residuated lattices that have height equal to 3 and show that the variety they generate has continuum-many subvarieties. More generally, we study unilinear residuated lattices: their lattice is a union of disjoint incomparable chains, with bounds added. We we give two general constructions of unilinear residuated lattices, provide an axiomatization and a proof-theoretic calculus for the variety they generate, and prove the finite model property for various subvarieties.
引用
收藏
页数：33
相关论文
共 50 条
  • [21] Amalgamation through quantifier elimination for varieties of commutative residuated lattices
    Enrico Marchioni
    Archive for Mathematical Logic, 2012, 51 : 15 - 34
  • [22] Amalgamation through quantifier elimination for varieties of commutative residuated lattices
    Marchioni, Enrico
    ARCHIVE FOR MATHEMATICAL LOGIC, 2012, 51 (1-2) : 15 - 34
  • [23] Logics Preserving Degrees of Truth from Varieties of Residuated Lattices
    Bou, Felix
    Esteva, Francesc
    Font, Josep Maria
    Gil, Angel J.
    Godo, Lluis
    Torrens, Antoni
    Verdu, Ventura
    JOURNAL OF LOGIC AND COMPUTATION, 2009, 19 (06) : 1031 - 1069
  • [24] Residuated lattices
    Ward, M
    Dilwort, RP
    PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1938, 24 : 162 - 164
  • [25] Residuated lattices
    Ward, Morgan
    Dilworth, R. P.
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1939, 45 (1-3) : 335 - 354
  • [26] Interpolation and FEP for logics of residuated algebras
    Buszkowski, Wojciech
    LOGIC JOURNAL OF THE IGPL, 2011, 19 (03) : 437 - 454
  • [27] Varieties of Commutative Integral Bounded Residuated Lattices Admitting a Boolean Retraction Term
    Roberto Cignoli
    Antoni Torrens
    Studia Logica, 2012, 100 : 1107 - 1136
  • [28] Varieties of Commutative Integral Bounded Residuated Lattices Admitting a Boolean Retraction Term
    Cignoli, Roberto
    Torrens, Antoni
    STUDIA LOGICA, 2012, 100 (06) : 1107 - 1136
  • [29] Factorization of residuated lattices
    Krupka, Michal
    LOGIC JOURNAL OF THE IGPL, 2009, 17 (02) : 205 - 223
  • [30] Skew residuated lattices
    Chajda, I.
    Krnavek, J.
    FUZZY SETS AND SYSTEMS, 2013, 222 : 78 - 83
12345