# The variety generated by all the ordinal sums of perfect MV-chains

We present the logic $\displaystyle BL_{Chang}$ , an axiomatic extension of BL (see [23]) whose corresponding algebras form the smallest variety containing all the ordinal sums of perfect MV-chains. We will analyze this logic and the corresponding algebraic semantics in the propositional and in the first-order case. As we will see, moreover, the variety of $\displaystyle BL_{Chang}$ -algebras will be strictly connected to the one generated by Chang’s MV-algebra (that is, the variety generated by all the perfect MV-algebras): we will also give some new results concerning these last structures and their logic.