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:
“Even in harmonious families there is this double life: the group life, which is the one we can observe in our neighbour’s household, and, underneath, another—secret and passionate and intense—which is the real life that stamps the faces and gives character to the voices of our friends. Always in his mind each member of these social units is escaping, running away, trying to break the net which circumstances and his own affections have woven about him.”
—Willa Cather (1873–1947)
“It makes no sense to say what the objects of a theory are,
beyond saying how to interpret or reinterpret that theory in another.”
—Willard Van Orman Quine (b. 1908)