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 marvel at the many ways we, as black people, bend but do not break in order to survive. This astonishes me, and what excites me I write about. Everyone of us is a wonder. Everyone of us has a story.”
    —Kristin Hunter (b. 1931)

    “The theory of rights enables us to rise and overthrow obstacles, but not to found a strong and lasting accord between all the elements which compose the nation.”
    —Giuseppe Mazzini (1805–1872)