---
tag: RQ52AJ3G1E
kind: concept
name: Jónsson function
sources:
  - wikipedia: en:18455668@r1246522851
    locator: Jónsson function
    note: adopted
    mention: wikipedia://en/18455668
    sections: [Summary]
same_as:
  wikidata: Q6320395
  wikipedia: Jónsson function
inventory: [4D3BQKKE03]
---

## Summary

In mathematical set theory, an **ω-Jónsson function** for a set *x* of [[ordinals|0RDJK7EQYY]] is a function $f:[x]^\omega\to x$ with the property that, for any subset *y* of *x* with the same [[cardinality|0G0ASKNA6Z]] as *x*, the restriction of $f$ to $[y]^\omega$ is [[surjective|01RVCMSN5N]] on $x$. Here $[x]^\omega$ denotes the set of strictly increasing sequences of members of $x$, or equivalently the family of subsets of $x$ with order type $\omega$, using a standard notation for the family of subsets with a given order type. Jónsson functions are named for Bjarni Jónsson.