---
tag: 4XPS4W1T1K
kind: concept
name: Computable isomorphism
aliases: [computably-isomorphic, recursive-isomorphism, recursively-isomorphic]
sources:
  - wikipedia: en:2611685@r1322667615
    locator: Computable isomorphism
    note: adopted
    mention: wikipedia://en/2611685
    sections: [Summary]
same_as:
  wikidata: Q5157265
  wikipedia: Computable isomorphism
inventory: [CM16KM9AT0]
---

## Summary

In computability theory two sets $A, B$ of [[natural numbers|0MWKJ44V5A]] are **computably isomorphic** or **recursively isomorphic** if there exists a total computable and bijective function $f \colon \mathbb{N} \to \mathbb{N}$ such that the image of $f$ restricted to $A\subseteq \mathbb{N}$ equals $B\subseteq \mathbb{N}$, i.e. $f(A) = B$.