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:

    Every philosophy is tinged with the colouring of some secret imaginative background, which never emerges explicitly into its train of reasoning.
    —Alfred North Whitehead (1861–1947)

    The problem of culture is seldom grasped correctly. The goal of a culture is not the greatest possible happiness of a people, nor is it the unhindered development of all their talents; instead, culture shows itself in the correct proportion of these developments. Its aim points beyond earthly happiness: the production of great works is the aim of culture.
    Friedrich Nietzsche (1844–1900)