THE FIRST-ORDER LOGIC OF CZF IS INTUITIONISTIC FIRST-ORDER LOGIC

@article{Passmann2021THEFL,
  title={THE FIRST-ORDER LOGIC OF CZF IS INTUITIONISTIC FIRST-ORDER LOGIC},
  author={Robert Passmann},
  journal={The Journal of Symbolic Logic},
  year={2021}
}
  • Robert Passmann
  • Published 1 December 2021
  • Philosophy, Computer Science
  • The Journal of Symbolic Logic
. We prove that the first-order logic of CZF is intuitionistic first-order logic. To do so, we introduce a new model of transfinite computation (Set Register Machines) and combine the resulting notion of realisability with Beth semantics. On the way, we also show that the propositional admissible rules of CZF are exactly those of intuitionistic propositional logic. 
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