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:
“A self is, by its very essence, a being with a past. One must look lengthwise backwards in the stream of time in order to see the self, or its shadow, now moving with the stream, now eddying in the currents from bank to bank of its channel, and now strenuously straining onwards in the pursuit of its chosen good.”
—Josiah Royce (1855–1916)
“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)