Uniqueness of the implication for totally ordered MV-algebras

It is shown that in a linearly ordered MV-algebra A, the implication is unique if and only if the identity function is the unique De Morgan automorphism on A. Modulo categorical equivalence, our uniqueness criterion recalls Ohkuma's rigidness condition for totally ordered abelian groups. We als...

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Detalles Bibliográficos
Autores principales: Martínez, N.G., Petrovich, A.
Formato: JOUR
Materias:
03G25
06D05
06E15
De Morgan algebras
MV-algebras
Priestley's duality
Rigidness
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_01680072_v108_n1-3_p261_Martinez
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_01680072_v108_n1-3_p261_Martinez
record_format dspace
spelling todo:paper_01680072_v108_n1-3_p261_Martinez2023-10-03T15:05:39Z Uniqueness of the implication for totally ordered MV-algebras Martínez, N.G. Petrovich, A. 03G25 06D05 06E15 De Morgan algebras MV-algebras Priestley's duality Rigidness It is shown that in a linearly ordered MV-algebra A, the implication is unique if and only if the identity function is the unique De Morgan automorphism on A. Modulo categorical equivalence, our uniqueness criterion recalls Ohkuma's rigidness condition for totally ordered abelian groups. We also show that, if A is an Archimedean totally ordered MV-algebra, then each non-trivial De Morgan automorphism of the underlying involutive lattice of A yields a new implication on A, which is not isomorphic to the original implication. © 2001 Elsevier Science B.V. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_01680072_v108_n1-3_p261_Martinez
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic 03G25
06D05
06E15
De Morgan algebras
MV-algebras
Priestley's duality
Rigidness
spellingShingle 03G25
06D05
06E15
De Morgan algebras
MV-algebras
Priestley's duality
Rigidness
Martínez, N.G.
Petrovich, A.
Uniqueness of the implication for totally ordered MV-algebras
topic_facet 03G25
06D05
06E15
De Morgan algebras
MV-algebras
Priestley's duality
Rigidness
description It is shown that in a linearly ordered MV-algebra A, the implication is unique if and only if the identity function is the unique De Morgan automorphism on A. Modulo categorical equivalence, our uniqueness criterion recalls Ohkuma's rigidness condition for totally ordered abelian groups. We also show that, if A is an Archimedean totally ordered MV-algebra, then each non-trivial De Morgan automorphism of the underlying involutive lattice of A yields a new implication on A, which is not isomorphic to the original implication. © 2001 Elsevier Science B.V.
format JOUR
author Martínez, N.G.
Petrovich, A.
author_facet Martínez, N.G.
Petrovich, A.
author_sort Martínez, N.G.
title Uniqueness of the implication for totally ordered MV-algebras
title_short Uniqueness of the implication for totally ordered MV-algebras
title_full Uniqueness of the implication for totally ordered MV-algebras
title_fullStr Uniqueness of the implication for totally ordered MV-algebras
title_full_unstemmed Uniqueness of the implication for totally ordered MV-algebras
title_sort uniqueness of the implication for totally ordered mv-algebras
url http://hdl.handle.net/20.500.12110/paper_01680072_v108_n1-3_p261_Martinez
work_keys_str_mv AT martinezng uniquenessoftheimplicationfortotallyorderedmvalgebras
AT petrovicha uniquenessoftheimplicationfortotallyorderedmvalgebras
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