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:
“Undoubtedly we have not questions to ask which are unanswerable. We must trust the perfection of the creation so far, as to believe that whatever curiosity the order of things has awakened in our minds, the order of things can satisfy. Every man’s condition is a solution in hieroglyphic to those inquiries he would put. He acts it as life, before he apprehends it as truth.”
—Ralph Waldo Emerson (1803–1882)
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—Pamela Patrick Novotny (20th century)