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:
“In England if something goes wrong—say, if one finds a skunk in the garden—he writes to the family solicitor, who proceeds to take the proper measures; whereas in America, you telephone the fire department. Each satisfies a characteristic need; in the English, love of order and legalistic procedure; and here in America, what you like is something vivid, and red, and swift.”
—Alfred North Whitehead (1861–1947)
“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)