[FOM] reducing higher to second order?

Roger Bishop Jones rbj01 at rbjones.com
Tue Jan 6 10:41:03 EST 2004

In connection with the reducibility of higher order logics
to second order logic

On Sunday 04 January 2004  3:49 pm, Marcus Rossberg wrote:

> It might be useful to emphasis the following limitations:
> (1) This result only applies to validities (as stated above by
> Professor Enderton), not to the consequence relation in
> general. (2) The proof relies on the domain being set-sized.

Is it also true to say that despite this reducibility
w-order logic is not interpretable in 2nd order logic
in the sense required when considering consistency
strength, and that the consistency of 2nd order logic
should be provable in w-order logic?

Roger Jones

- rbj01 at rbjones.com
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