---
tag: 1C8ZVDSQXT
kind: statement
role: proposition
name: Tarski's theorem about choice
aliases: [tarskis-theorem-on-choice]
sources:
  - wikipedia: en:320578@r1336022373
    locator: Tarski's theorem about choice
    note: adopted
    mention: wikipedia://en/320578
    sections: [Statement]
same_as:
  wikidata: Q2908743
  wikipedia: Tarski's theorem about choice
inventory: [7WV5PH2EG9]
---

## Statement

In mathematics, **Tarski's theorem**, proved by (txt), states that in [[ZF|0HE5WDQ9FJ]] the statement "For every infinite set $A$, there is a bijective map between the sets $A$ and $A\times A$" implies the [[axiom of choice|0HTGB13FE2]]. The opposite direction was already known (provable via an explicit [[pairing function for any aleph number|0NP5N5PYW5]]), thus the statement and axiom of choice are equivalent.