Embeddings of totally ordered MV-algebras of bounded cardinality
Volume 203 / 2009
Fundamenta Mathematicae 203 (2009), 57-63
MSC: 06D35, 06F20.
DOI: 10.4064/fm203-1-5
Abstract
For a given cardinal number $\mathfrak{a}$, we construct a totally ordered MV-algebra $M(\mathfrak{a})$ having the property that every totally ordered MV-algebra of cardinality at most $\mathfrak{a}$ embeds into $M(\mathfrak{a})$. In case $\mathfrak{a} = \aleph_0$, the algebra $M(\mathfrak{a})$ is the first known MV-algebra with respect to which the deductive system for the infinitely-valued Łukasiewicz's propositional logic is strongly complete.
