The basic intuitionistic logic of proofs

@article{Artmov2007TheBI,
  title={The basic intuitionistic logic of proofs},
  author={Sergei N. Art{\"e}mov and Rosalie Iemhoff},
  journal={J. Symb. Log.},
  year={2007},
  volume={72},
  pages={439-451}
}
The language of the basic logic of proofs extends the usual propositional language by forming sentences of the sort x is a proof of F for any sentence F . In this paper a complete axiomatization for the basic logic of proofs in Heyting Arithmetic HA was found. 

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