I am familiar with the concept that a statement can be proven indepent such as in the case of the continuum hypothesis where both ZFC+CH and ZFC+(CH is false) are both proven consistent, but I would like to know if any current publications show that ZFC can show the following to be true of a statement T:
[ZFC+T is cconsistent and ZFC+(T is false) is consistent] is independent
(I apologize at how informally the question is posed; I've just started to read the work of Cohen and Godel and have been unable to find any text refering to this problem)