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.