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:
“Knowing what [Christ] knew , knowing all about mankind—ah! who would have thought that the crime is not so much to make others die, but to die oneself—confronted day and night with his innocent crime, it became too difficult to go on. It was better to get it over with, to not defend himself, to die, in order not to be the only one to have survived, and to go elsewhere, where, perhaps, he would be supported.”
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