Semilinear substructural logics with the finite embeddability property

Abstract

Three semilinear substructural logics $${\mathbf{HpsUL}}_\omega ^*$$ , $${\mathbf{UL}}_\omega $$ and $${\mathbf{IUL}}_\omega $$ are constructed. Then the completeness of $${ \mathbf{UL}}_\omega $$ and $${\mathbf{IUL}}_\omega $$ with respect to classes of finite UL and IUL-algebras, respectively, is proved. Algebraically, non-integral $${\mathbf{UL}}_\omega $$ and $${\mathbf{IUL}}_\omega $$ -algebras have the finite embeddability property, which gives a characterization for finite UL and IUL-algebras.