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Universal Classes of MV‐chains with Applications to Many‐valued Logics
Author(s) -
Gispert Joan
Publication year - 2002
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/1521-3870(200211)48:4<581::aid-malq581>3.0.co;2-w
Subject(s) - finitary , mathematics , distributive property , congruence (geometry) , characterization (materials science) , propositional calculus , algebra over a field , łukasiewicz logic , class (philosophy) , discrete mathematics , pure mathematics , intermediate logic , substructural logic , computer science , theoretical computer science , artificial intelligence , description logic , materials science , geometry , nanotechnology
In this paper we characterize, classify and axiomatize all universal classes of MV‐chains. Moreover, we accomplish analogous characterization, classification and axiomatization for congruence distributive quasivarieties of MV‐algebras. Finally, we apply those results to study some finitary extensions of the Łukasiewicz infinite valued propositional calculus.