FOM: Finitely axiomatizable fragments of set theory

[Richard G. Heck, Jr.]

>A final question: ZF proves the consistency of any finitely axiomatizable 
>subtheory of itself.  Do Z and PA also have this property?

Certainly PA has this property, since PA proves Con(PA(n)), for all n, 
where PA(n) has induction for just the sigma-n formulae.

rh

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Richard G. Heck Jr.
http://www.people.fas.harvard.edu/~heck