Roman Legion in late Antiquity

[Nathan Ross]

at which point or under which Emperor were legions established as consisting of 6000 men?

I think Septimius Severus is supposed to have increased the size of the legion, perhaps just by increasing the cavalry component (equites legionis, later equites promoti when they started operating as detached units).

If you want a brief precis of the current state of theory (!) then something like this might work:

In the earlier imperial period (1st-2nd centuries AD) the century comprised around 80 men, with six centuries making up a cohort and ten cohorts a legion. The emperor Severus increased the size of the legion, but after this point most legions operated in detachments of one or two cohorts. By the 4th century, some of these detachments (vexillations) became legions in their own right, providing a model for the new units of the imperial field army which comprised around 1000 men each.

It's still very general, a bit confusing, and glosses over difficult issues like the size of the later century and the internal organisation of the new 'legions', but it might do, depending what you need it for...