Math 2.0

Proposition

Tarski's theorem about choice

Statement

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

Reading path

To understand this page from the ground up, read these 2 pages in order. The foundations come first. The path takes the proof Proof of Tarski's theorem about choice.

Show the path as a graph
Proof of Tarski's theorem about choice, proof, no evidence levelProof of Tarski's the…proofTarski's theorem about choice, statement, no evidence levelTarski's theorem abou…statement
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Proof of Tarski's theorem about choice proof
  2. Tarski's theorem about choice statement

Further reading

  1. Wikipedia, page 320578, revision 1336022373, Tarski's theorem about choice. adopted
About this page
Tag1C8ZVDSQXT
URIm2://1C8ZVDSQXT
Aliasestarskis-theorem-on-choice
Kindstatement, proposition
WritingW0 stub
StatusThis copy of the site has no build data. Run m2 status 1C8ZVDSQXT.
Same as
Changed4 November 2026

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What this page needs for W1

  • edge uses out: each definition that the statement needs (0 of 1)

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What links here

Proofs