Mundici has recently established a characterization of free finitely generated MV-algebras similar in spirit to the representation of the free Boolean algebra with a countably infinite set of free generators as any Boolean algebra that is countable and atomless. No reference to universal properties is made in either theorem. Our main result is an extension of Mundici’s theorem to the whole class of MV-algebras that are free over some finite distributive lattice.
A characterization of MV-algebras free over finite distributive lattices / V. Marra. - In: ARCHIVE FOR MATHEMATICAL LOGIC. - ISSN 0933-5846. - 47:3(2008 Jul), pp. 263-276.
A characterization of MV-algebras free over finite distributive lattices
V. MarraPrimo
2008
Abstract
Mundici has recently established a characterization of free finitely generated MV-algebras similar in spirit to the representation of the free Boolean algebra with a countably infinite set of free generators as any Boolean algebra that is countable and atomless. No reference to universal properties is made in either theorem. Our main result is an extension of Mundici’s theorem to the whole class of MV-algebras that are free over some finite distributive lattice.
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