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Reports on Mathematical Logic

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No. 34

Katarzyna PALASINSKA

Sequent calculi and quasivarieties
A b s t r a c t.
We discuss quasivarieties related in some special sense to sequent
calculi. We show that the free algebra in such a \qv\ is Fregean iff the
sequent calculus has so-called {\it symmetric contraction} rules admissible.
In the presence of the fusion connective this is equivalent to having
contraction. With every sequent calculus $\cG$ one can associate, in some
way, a sequent calculus with fusion. If this calculus has a separability
property then a quasivariety $\Q$ related to $\cG$ is the class of fusion-less
reducts of some quasivariety of algebras with fusion.

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