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:
“Explanations comfort us by giving the impression that there is an order in things.”
—Mason Cooley (b. 1927)
“The weakness of the man who, when his theory works out into a flagrant contradiction of the facts, concludes So much the worse for the facts: let them be altered, instead of So much the worse for my theory.”
—George Bernard Shaw (18561950)
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