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Girard's recent system of linear logic is presented in a way that avoids the two-level structure of formulae and sequents, and that minimises the number of primitive function symbols. A deduction theorem is proved concerning the classical implication as embedded in linear logic. The Hilbertstyle axiomatisation is proved to be equivalent to the sequent formalism. The axiomatisation leads to a complete class of algebraic models. Various models are exhibited. On the meta-level we use Dijkstra'sdoi:10.1007/bf01888221 fatcat:ic7vezgsubaiphq7h6ttojjrgy