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

Abstract

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 Rad(A) is a divisible monoid and A/Rad(A) is either finite or divisible. © 2013 Elsevier B.V.