In this paper, constructions of free algebras corresponding to multiplicative classical linear logic, its affine variant, and their extensions with $n$-contraction ($n\geq 2$) are given. As an application, the cardinality problem of some one-variable linear fragments with $n$-contraction is solved.
"Free Algebras Corresponding to Multiplicative Classical Linear Logic and Some of Its Extensions." Notre Dame J. Formal Logic 37 (1) 53 - 70, Winter 1996. https://doi.org/10.1305/ndjfl/1040067316