number realizability

The version of realizability where truth/proof is realized by numbers.

As opposed to *function realizability*.

type I computability | type II computability | |
---|---|---|

typical domain | natural numbers $\mathbb{N}$ | Baire space of infinite sequences $\mathbb{B} = \mathbb{N}^{\mathbb{N}}$ |

computable functions | partial recursive function | computable function (analysis) |

type of computable mathematics | recursive mathematics | computable analysis, Type Two Theory of Effectivity |

type of realizability | number realizability | function realizability |

partial combinatory algebra | Kleene's first partial combinatory algebra | Kleene's second partial combinatory algebra |