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:
“In Russia there is an emigration of intelligence: émigrés cross the frontier in order to read and to write good books. But in doing so they contribute to making their fatherland, abandoned by spirit, into the gaping jaws of Asia that would like to swallow our little Europe.”
—Friedrich Nietzsche (1844–1900)
“Freud was a hero. He descended to the “Underworld” and met there stark terrors. He carried with him his theory as a Medusa’s head which turned these terrors to stone.”
—R.D. (Ronald David)