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 a suitable language if and only if Rad(A) is a divisible monoid and A/Rad(A) is either finite or divisible.
An Algebraic Characterization of O-Minimal and Weakly O-Minimal MV-Chains
LENZI, Giacomo;
2014
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 a suitable language if and only if Rad(A) is a divisible monoid and A/Rad(A) is either finite or divisible.File in questo prodotto:
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