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.