The problem with the 'standard' definition we so often encounter in discussions of DOF however is that it is not that of DOF, but of hyperfocal distance.
Again, it is just f-stop and magnification, but it's magnification at the point whose focus is being considered, NOT magnification at the plane of best focus. Since you can't keep all of the magnifications the same for different FsoV you get different DoF results.
I fully agree that none of the other things are related to DoF in the least, only to "apparent" DoF which is purely subjective.
Field of View is a function of format if other factors are the same, and if those factors are the same the actual properties of DoF will be identical. The subjective effect might be quite different however, say between 100mm on minox vs 8x10 inches. The minox frame will offer the same properties within a severely cropped area and appear as a compressed telephoto lens. The 8x10 will be very wide and offer the perspective of and focus characteristic of a very wide focal length. This is because the perspective of a focal length is relative to the format. Folks tend to forget this. To offer the same FoV between formats one must change the lens or distance and focus, and you are no longer comparing anything meaningful concerning DoF, not that it's overly meaningful the other way either.
The CoC for a given format ,focus, focal length, and stop allows one to calculate DoF in a practical way (there's that word again) I seldom calculate for stills because I can see it, but for motion picture where things are very fluid and judgments by eye can be very difficult I use a thing called a SamCine calculator. Basically a slide rule that allows you to calculate DoF for different format/focal/t-stop combinations using CoC as the objective criteria. Understanding the CoC implications for a chosen format is important to using the device. Where the CoC remains the same it will not have the same visual effect as a practical matter across formats, regardless of your subjectivity or objectivity, therefore CoC alone doesn't tell you anything. It's more than just about subjective/objective, it is about practical application, and there isn't some magic bullet formula that you can carry in your pocket that applies across the board. A only a working knowledge and experience can really inform. In other words, get out and shoot. A couple of exposures are worth more than all the words in this thread, mine included.
That's exactly it: a practical matter.
Forget all formulae and calculators, and use your eyes (is photography a visual medium?)
Select a subject. Decide what your picture is about.
Focus on that subject.
Then use the aperture to set how it relates visually to the rest of what is in the frame, judging not by table or scale, but by looking through the viewfinder to see how the sharp vs unsharp balance changes.
Yes, it is difficult when the groundglass gets darker and darker. But then, who promised it would be easy?
And to all those who say their subject stretches from the front lens to infinity, my response would be that such images are boring, and perhaps need not be produced in the first place. Just my view :D
But if you want to produce images without deciding what they are of anyway, just stop the lens down as far as it goes and be done with it.
But whatever you do, do not even think about DOF as a quantifiable entity. As something that can be discussed and decided upon separately, apart from the particular image your lens is projecting on your screen.
It quite simply is not.
It will always be either too much, too little, or just right.
But how much that is, is different every single time you create an image.
So just use your eyes and look.
I have posted in the past that while I was studying optics at Kodak, that I raised the question about why when I kept the image size and exposures settings the same, I could not get a better depth of field by changing lenses. The optical engineer started with the depth of field equation and made one substitution. Four lines later the focal length was in every term and then was divided out. The result is exactly as Q.G. stated.
When magnification and f-stop are constant, DOF will be too, no matter how large or small the frame.