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:

    “Art is the imposing of a pattern on experience, and our aesthetic enjoyment is recognition of the pattern.”
    —Alfred North Whitehead (1861–1947)

    “A curious thing about the ontological problem is its simplicity. It can be put in three Anglo-Saxon monosyllables: ‘What is there?’ It can be answered, moveover, in a word—‘Everything.’”
    —Willard Van Orman Quine (b. 1908)