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:
“No group and no government can properly prescribe precisely what should constitute the body of knowledge with which true education is concerned.”
—Franklin D. Roosevelt (1882–1945)
“We commonly say that the rich man can speak the truth, can afford honesty, can afford independence of opinion and action;—and that is the theory of nobility. But it is the rich man in a true sense, that is to say, not the man of large income and large expenditure, but solely the man whose outlay is less than his income and is steadily kept so.”
—Ralph Waldo Emerson (1803–1882)