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:
“Power corrupts ... when the weak band together in order to ruin the strong, but not before. The will to power ... far from being a characteristic of the strong, is, like envy and greed, among the vices of the weak, and possibly even their most dangerous one.”
—Hannah Arendt (1906–1975)
“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)