Amalgamation in classes of involutive commutative residuated lattices

Sándor Jenei

Published 2020-12-28Version 1

The amalgamation property and its variants are in strong relationship with various syntactic interpolation properties of substructural logics, hence its investigation in varieties of residuated lattices is of particular interest. The amalgamation property is investigated in some classes of non-divisible, non-integral, and non-idempotent involutive commutative residuated lattices in this paper. It is proved that the classes of odd and even totally ordered, involutive, commutative residuated lattices fail the amalgamation property. It is also proved that the varieties of odd and even semilinear, idempotent symmetric, involutive, commutative residuated lattices have the amalgamation property, and hence also the transferable injections property.