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:
“When I behold a rich landscape, it is less to my purpose to recite correctly the order and superposition of the strata, than to know why all thought of multitude is lost in a tranquil sense of unity.”
—Ralph Waldo Emerson (1803–1882)
“The struggle for existence holds as much in the intellectual as in the physical world. A theory is a species of thinking, and its right to exist is coextensive with its power of resisting extinction by its rivals.”
—Thomas Henry Huxley (1825–95)