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 it is owing to their wonder that men both now begin and at first began to philosophize.... And a man who is puzzled and wonders thinks himself ignorant ...; therefore since they philosophized in order to escape from ignorance, evidently they were pursuing science in order to know, and not for any utilitarian end.”
—Aristotle (384–322 B.C.)
“It is not enough for theory to describe and analyse, it must itself be an event in the universe it describes. In order to do this theory must partake of and become the acceleration of this logic. It must tear itself from all referents and take pride only in the future. Theory must operate on time at the cost of a deliberate distortion of present reality.”
—Jean Baudrillard (b. 1929)