Whitehead Problem

In group theory, a branch of abstract algebra, the Whitehead problem is the following question:

Is every abelian group A with Ext1(A, Z) = 0 a free abelian group?

Shelah (1974) proved that Whitehead's problem is undecidable within standard ZFC set theory.

Read more about Whitehead Problem:  Refinement, Shelah's Proof, Discussion

Famous quotes containing the words whitehead and/or problem:

    Life is an offensive, directed against the repetitious mechanism of the Universe.
    —Alfred North Whitehead (1861–1947)

    To make a good salad is to be a brilliant diplomatist—the problem is entirely the same in both cases. To know exactly how much oil one must put with one’s vinegar.
    Oscar Wilde (1854–1900)