An algebraic characterization of o-minimal and weakly o-minimal MV-chains

We present an algebraic characterization of both o-minimal and weakly o-minimal MV-chains by showing that a linearly ordered MV-algebra is (1) o-minimal if and only if it is finite or divisible, and (2) weakly o-minimal if and only if its first-order theory admits quantifier elimination in the language 〈⊕,∗,0〉 if and only if is a divisible monoid and is either finite or divisible.