Parametric Church's Thesis: Synthetic Computability Without Choice

  title={Parametric Church's Thesis: Synthetic Computability Without Choice},
  author={Yannick Forster},
  • Y. Forster
  • Published 16 December 2021
  • Philosophy
  • ArXiv
In synthetic computability, pioneered by Richman, Bridges, and Bauer, one develops computability theory without an explicit model of computation. This is enabled by assuming an axiom equivalent to postulating a function φ to be universal for the space N→N (CTφ, a consequence of the constructivist axiom CT), Markov’s principle, and at least the axiom of countable choice. Assuming CT and countable choice invalidates the law of excluded middle, thereby also invalidating classical intuitions… 
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