[FOM] n-th order ZFC

[W.Taylor at math.canterbury.ac.nz]

Quoting pax0 at seznam.cz:

> Is there ANY USEFUL SITUATION which would mention
> n-th order ZFC
> for n>=3?
> Thank you, Jan Pax

And may I add a further related query.

I have read long ago that in some sense 3rd-order (or higher) is unnecessary,
in that 3rd-order can be somehow "mirrored" in second-order, with no loss
of fidelity.  Or some such comment.

Can anyone elaborate on that?  And give us a brief idea of how such
a coding is effected?

TIA   -- Wondering William


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