Order Theory
The answer to Suslin's problem is independent of ZFC. The diamond principle ◊ proves the existence of a Suslin line, while MA + ¬CH proves that no Suslin line exists.
Existence of Kurepa trees is independent of ZFC.
Read more about this topic: List Of Statements Undecidable In ZFC
Famous quotes containing the words order and/or theory:
“The confusion of emotions with behavior causes no end of unnecessary trouble to both adults and children. Behavior can be commanded; emotions can’t. An adult can put controls on a child’s behavior—at least part of the time—but how do you put controls on what a child feels? An adult can impose controls on his own behavior—if he’s grown up—but how does he order what he feels?”
—Leontine Young (20th century)
“The theory seems to be that so long as a man is a failure he is one of God’s chillun, but that as soon as he has any luck he owes it to the Devil.”
—H.L. (Henry Lewis)