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:
“To me the “female principle” is, or at least historically has been, basically anarchic. It values order without constraint, rule by custom not by force. It has been the male who enforces order, who constructs power structures, who makes, enforces, and breaks laws.”
—Ursula K. Le Guin (b. 1929)
“every subjective phenomenon is essentially connected with a single point of view, and it seems inevitable that an objective, physical theory will abandon that point of view.”
—Thomas Nagel (b. 1938)