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:
“I don’t know but a book in a man’s brain is better off than a book bound in calf—at any rate it is safer from criticism. And taking a book off the brain, is akin to the ticklish & dangerous business of taking an old painting off a panel—you have to scrape off the whole brain in order to get at it with due safety—& even then, the painting may not be worth the trouble.”
—Herman Melville (1819–1891)
“If my theory of relativity is proven correct, Germany will claim me as a German and France will declare that I am a citizen of the world. Should my theory prove untrue, France will say that I am a German and Germany will declare that I am a Jew.”
—Albert Einstein (1879–1955)