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:
“While I am in favor of the Government promptly enforcing the laws for the present, defending the forts and collecting the revenue, I am not in favor of a war policy with a view to the conquest of any of the slave States; except such as are needed to give us a good boundary. If Maryland attempts to go off, suppress her in order to save the Potomac and the District of Columbia. Cut a piece off of western Virginia and keep Missouri and all the Territories.”
—Rutherford Birchard Hayes (1822–1893)
“The things that will destroy America are prosperity-at-any- price, peace-at-any-price, safety-first instead of duty-first, the love of soft living, and the get-rich-quick theory of life.”
—Theodore Roosevelt (1858–1919)