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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2001
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paper:paper_01680072_v108_n1-3_p261_Martinez2023-06-08T15:17:11Z Uniqueness of the implication for totally ordered MV-algebras 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. 2001 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01680072_v108_n1-3_p261_Martinez 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 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. |
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 |
publishDate |
2001 |
url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01680072_v108_n1-3_p261_Martinez http://hdl.handle.net/20.500.12110/paper_01680072_v108_n1-3_p261_Martinez |
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1768544773742788608 |