Archive for September 29th, 2006

Whitehead problem

Friday, September 29th, 2006

I was reading Hilton and Stammbach’s A Course in Homological Algebra, when I spotted this rather forlorn passage:

Of course, if A is free, Ext(A,Z) = 0, but it is still an open question whether, for all abelian groups A, Ext(A,Z) = 0 implies A free.

It is forlorn because we now know that we’ll never know: this is the Whitehead problem, and in 1973 Saharon Shelah proved that it is independent of the axioms of set theory.

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