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:

    “Beauty is desired in order that it may be befouled; not for its own sake, but for the joy brought by the certainty of profaning it.”
    —Georges Bataille (1897–1962)

    “The things that will destroy America are prosperity-at-any- price, peace-at-any-price, safety-first instead of duty-first, the love of soft living, and the get-rich-quick theory of life.”
    —Theodore Roosevelt (1858–1919)