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:

    “The one book necessary to be understood by a divine, is the Bible; any others are to be read, chiefly, in order to understand that.”
    —Francis Lockier (1668–1740)

    “No theory is good unless it permits, not rest, but the greatest work. No theory is good except on condition that one use it to go on beyond.”
    —André Gide (1869–1951)