Sequent Calculus in the Topos of Trees

@article{Clouston2015SequentCI,
  title={Sequent Calculus in the Topos of Trees},
  author={Ranald Clouston and Rajeev Gor{\'e}},
  journal={ArXiv},
  year={2015},
  volume={abs/1501.03293}
}
Nakano’s “later” modality, inspired by Godel-Lob provability logic, has been applied in type systems and program logics to capture guarded recursion. Birkedal et al modelled this modality via the internal logic of the topos of trees. We show that the semantics of the propositional fragment of this logic can be given by linear converse-well-founded intuitionistic Kripke frames, so this logic is a marriage of the intuitionistic modal logic KM and the intermediate logic LC. We therefore call this… 

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