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:
“All the sciences are now under an obligation to prepare for the future task of philosopher, which is to solve the problem of value, to determine the rank order of values.”
—Friedrich Nietzsche (1844–1900)
“There could be no fairer destiny for any physical theory than that it should point the way to a more comprehensive theory in which it lives on as a limiting case.”
—Albert Einstein (1879–1955)
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