---
tag: 1HXBZNJQDX
kind: concept
name: Computably inseparable
aliases: [computably-inseparable-sets, effectively-inseparable, effectively-inseparable-sets, effectively-separable, effectively-separable-set, effectively-separable-sets, recursive-inseparability, recursively-inseparable, recursively-inseparable-sets, recursively-separable, recursively-separable-sets]
sources:
  - wikipedia: en:26004614@r1298641139
    locator: Computably inseparable
    note: adopted
    mention: wikipedia://en/26004614
    sections: [Summary]
same_as:
  wikidata: Q7303355
  wikipedia: Computably inseparable
inventory: [SSRVGHP7Y5]
---

## Summary

In computability theory, two [[disjoint sets|0W4RPA8QH3]] of natural numbers are called **computably inseparable** or **recursively inseparable** if they cannot be "separated" with a computable set. These sets arise in the study of computability theory itself, particularly in relation to $\Pi^0_1$ classes. Computably inseparable sets also arise in the study of Gödel's incompleteness theorem.