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:

    “I knew I had to do it. It was an order from the coach.”
    —Charlotte Smith (b. 1974)

    “Every theory is a self-fulfilling prophecy that orders experience into the framework it provides.”
    —Ruth Hubbard (b. 1924)