Intuitionistic completeness of first-order logic

@article{Constable2014IntuitionisticCO,
  title={Intuitionistic completeness of first-order logic},
  author={Robert L. Constable and Mark Bickford},
  journal={Ann. Pure Appl. Log.},
  year={2014},
  volume={165},
  pages={164-198}
}
Abstract We constructively prove completeness for intuitionistic first-order logic, iFOL, showing that a formula is provable in iFOL if and only if it is uniformly valid in intuitionistic evidence semantics as defined in intuitionistic type theory extended with an intersection operator. Our completeness proof provides an effective procedure that converts any uniform evidence into a formal iFOL proof. Uniform evidence can involve arbitrary concepts from type theory such as ordinals, topological… 
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