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 Republicans] offer ... a detailed agenda for national renewal.... [On] reducing illegitimacy ... the state will use ... funds for programs to reduce out-of-wedlock pregnancies, to promote adoption, to establish and operate children’s group homes, to establish and operate residential group homes for unwed mothers, or for any purpose the state deems appropriate. None of the taxpayer funds may be used for abortion services or abortion counseling.”
—Newt Gingrich (b. 1943)
“No one thinks anything silly is suitable when they are an adolescent. Such an enormous share of their own behavior is silly that they lose all proper perspective on silliness, like a baker who is nauseated by the sight of his own eclairs. This provides another good argument for the emerging theory that the best use of cryogenics is to freeze all human beings when they are between the ages of twelve and nineteen.”
—Anna Quindlen (20th century)