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# Contraction-free sequent calculi for geometric theories with an application to Barr's theorem

@article{Negri2003ContractionfreeSC, title={Contraction-free sequent calculi for geometric theories with an application to Barr's theorem}, author={Sara Negri}, journal={Arch. Math. Log.}, year={2003}, volume={42}, pages={389-401} }

- Published 2003 in Arch. Math. Log.
DOI:10.1007/s001530100124

Geometric theories are presented as contractionand cut-free systems of sequent calculi with mathematical rules following a prescribed rule-scheme that extends the scheme given in Negri and von Plato (1998). Examples include cut-free calculi for Robinson arithmetic and real closed fields. As an immediate consequence of cut elimination, it is shown that if a geometric implication is classically derivable from a geometric theory then it is intuitionistically derivable.