The statement every filter in a Boolean algebra can be extended to an ultrafilter is called the Ultrafilter Theorem .
The statement every filter in a Boolean algebra can be extended to an ultrafilter is can not be proved in ZF , if ZF is consistent .
The statement every filter in a Boolean algebra can be extended to an ultrafilter is called the Ultrafilter Theorem and can not be proved in ZF , if ZF is consistent .