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:
“You listen to artists fighting with each other, competing to the death like gladiators, in order to see who is going to get into a show, who is going to make it, who isn’t: who is going to get a full-page ad and who is going to get a half-page. Then I think, “Wouldn’t it be wonderful to go off somewhere and just do your work?””
—Howardena Pindell (b. 1943)
“... the first reason for psychology’s failure to understand what people are and how they act, is that clinicians and psychiatrists, who are generally the theoreticians on these matters, have essentially made up myths without any evidence to support them; the second reason for psychology’s failure is that personality theory has looked for inner traits when it should have been looking for social context.”
—Naomi Weisstein (b. 1939)