Embeddings of totally ordered MV-algebras of bounded cardinality

Volume 203 / 2009

Piotr J. Wojciechowski Fundamenta Mathematicae 203 (2009), 57-63 MSC: 06D35, 06F20. DOI: 10.4064/fm203-1-5


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.


  • Piotr J. WojciechowskiDepartment of Mathematical Sciences
    The University of Texas at El Paso
    El Paso, TX 79968, U.S.A.

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