List of Statements Undecidable in ZFC - Order Theory

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:

    “It is with unfathomable love, pure joy and no regret that we leave this world. Men, do not cry for our fate, but cry for your own.”
    —Members of the Order of the Solar T.. New York Times, p. 1 (October l4, 1994)

    “The theory of the Communists may be summed up in the single sentence: Abolition of private property.”
    —Karl Marx (1818–1883)