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Lattice ordered groups and algebras of logic

SPEAKER: Jean Bernard Nganou

TITLE: Lattice ordered groups and algebras of logic

ABSTRACT: MV-algebras were introduced in the 1930’s by C. Chang as the algebraic counterpart of Lukasiewicz’s Many-value logic. MV-algebras are BL-algebras whose negations are involutions. For any BL-algebra $L$, we construct an associated lattice ordered Abelian group $G_L$ that coincides with the Chang’s $ell$-group of an MV-algebra when the BL-algebra is an MV-algebra. We prove that the Chang-Mundici’s group of the MV-center of any BL-algebra $L$ is a direct summand in $G_L$. We also find a direct description of the complement $mathfrak{S}(L)$ of the Chang’s group of the MV-center in terms of the filter of dense elements of $L$. Finally, we compute some examples of the group $G_L$.

This is a joint work with C. Lele.