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:
“Without poets, without artists, men would soon weary of nature’s monotony. The sublime idea men have of the universe would collapse with dizzying speed. The order which we find in nature, and which is only an effect of art, would at once vanish. Everything would break up in chaos. There would be no seasons, no civilization, no thought, no humanity; even life would give way, and the impotent void would reign everywhere.”
—Guillaume Apollinaire (1880–1918)
“[Anarchism] is the philosophy of the sovereignty of the individual. It is the theory of social harmony. It is the great, surging, living truth that is reconstructing the world, and that will usher in the Dawn.”
—Emma Goldman (1869–1940)