# Parametric Church's Thesis: Synthetic Computability Without Choice

@article{Forster2022ParametricCT, title={Parametric Church's Thesis: Synthetic Computability Without Choice}, author={Yannick Forster}, journal={ArXiv}, year={2022}, volume={abs/2112.11781} }

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…

## 2 Citations

Towards a Mechanized Theory of Computation for Education

- Computer Science
- 2022

This project includes full proofs of results from a textbook, such as the undecidability of the halting problem and Rice’s theorem, and presents a simple and expressive calculus that allows for the essence of informal proofs of classic theorems in a mechanized setting.

Synthetic Turing Reducibility in CIC

- Computer Science
- 2022

A definition of Turing reducibility in synthetic computability carried out in CIC, the type theory underlying Coq, is discussed, allowing for a defined via continuous Turing functionals based on an idea of Bauer.

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