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}
}
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. 

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