For a given cardinal number 𝔞, we construct a totally ordered MV-algebra M(𝔞) having the property that every totally ordered MV-algebra of cardinality at most 𝔞 embeds into M(𝔞). In case 𝔞 = ℵ₀, the algebra M(𝔞) is the first known MV-algebra with respect to which the deductive system for the infinitely-valued Łukasiewicz's propositional logic is strongly complete.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-1-5,
author = {Piotr J. Wojciechowski},
title = {Embeddings of totally ordered MV-algebras of bounded cardinality},
journal = {Fundamenta Mathematicae},
volume = {205},
year = {2009},
pages = {57-63},
zbl = {1174.06016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-1-5}
}
Piotr J. Wojciechowski. Embeddings of totally ordered MV-algebras of bounded cardinality. Fundamenta Mathematicae, Tome 205 (2009) pp. 57-63. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-1-5/