Strongly algebraically closed lattices in $\ell$-groups and semilattices

In this article, the properties of being $\aleph_0$-classes of a full $\ell$-group, the set of polars of an $\ell$-group, the complemented $\ell$-ideals of a complete $\ell$-group, the set of invariant elements of a dimension ortholattice, and pseudocomplemented semilattices are studied from the perspective of model theory and their relations to strongly algebraically closed lattices are obtained.