# Whitehead problem

- kind: problem
- status: independent (evidence tier V3)
- year: 1950
- authors: J. H. C. Whitehead

**Statement.** Is every abelian group A with Ext(A, Z) = 0 a free abelian group?

An ordinary-looking question in algebra turned out to have no answer in standard set theory. It is true under V = L and false under Martin's axiom with the continuum hypothesis false. It was the first major problem from outside logic shown independent.

*Evidence tier V3 is the import default for a result the curation records as settled in the published record. No formal proof or certificate is attached to this page yet.*

Posed 1950s, J. H. C. Whitehead. Closed 1974, Saharon Shelah: independent of ZFC.

## Sources

- [Wikipedia: Whitehead problem](https://en.wikipedia.org/wiki/Whitehead_problem)

[Logic and foundations](/wiki/Space:logic-foundations.md) · [Mathematics](/wiki/Continent:mathematics.md)

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