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:

    For man is but the servant and interpreter of nature: what he does and what he knows is only what he has observed of nature’s order in fact or in thought; beyond this he knows nothing and can do nothing.
    Francis Bacon (1560–1626)

    Frankly, these days, without a theory to go with it, I can’t see a painting.
    Tom Wolfe (b. 1931)