Realizability interpretation of PA by iterated limiting PCA

@article{Akama2014RealizabilityIO,
  title={Realizability interpretation of PA by iterated limiting PCA},
  author={Y. Akama},
  journal={Mathematical Structures in Computer Science},
  year={2014},
  volume={24}
}
  • Y. Akama
  • Published 2014
  • Computer Science, Mathematics
  • Mathematical Structures in Computer Science
For any partial combinatory algebra (PCA for short) $\mathcal{A}$, the class of $\mathcal{A}$-representable partial functions from $\mathbb{N}$ to $\mathcal{A}$ quotiented by the filter of cofinite sets of $\mathbb{N}$ is a PCA such that the representable partial functions are exactly the limiting partial functions of $\mathcal{A}$-representable partial functions (Akama 2004). The n-times iteration of this construction results in a PCA that represents any n-iterated limiting partial recursive… Expand
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