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:
““New order of the ages” did we say?
If it looks none too orderly today,
‘Tis a confusion it was ours to start
So in it have to take courageous part.”
—Robert Frost (1874–1963)
“Every theory is a self-fulfilling prophecy that orders experience into the framework it provides.”
—Ruth Hubbard (b. 1924)
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