Group Theory
In 1973, Saharon Shelah showed that the Whitehead problem ("is every abelian group A with Ext1(A, Z) = 0 a free abelian group?") is independent of ZFC. A group with Ext1(A, Z) = 0 which is not free abelian is called a Whitehead group; MA + ¬CH proves the existence of a Whitehead group, while V = L proves that no Whitehead group exists.
Read more about this topic: List Of Statements Undecidable In ZFC
Famous quotes containing the words group and/or theory:
“The poet who speaks out of the deepest instincts of man will be heard. The poet who creates a myth beyond the power of man to realize is gagged at the peril of the group that binds him. He is the true revolutionary: he builds a new world.”
—Babette Deutsch (1895–1982)
“The theory of rights enables us to rise and overthrow obstacles, but not to found a strong and lasting accord between all the elements which compose the nation.”
—Giuseppe Mazzini (1805–1872)