[FOM] Weak independent statements of arithmetic

Colin McLarty colin.mclarty at case.edu
Tue Feb 23 08:34:08 EST 2010

This may be very familiar but I do not know it:  what is known about
new axioms which can be added to ZFC without increasing the
consistency strength (as for example CH, or V\neq L, or Martin's
axiom) but which do imply first order statements of arithmetic which
are not implied by ZFC alone?

Well, one example would be any statement of first order arithmetic
which is independent of ZFC but provably equiconsistent with it.  I do
not care if the equiconsistency proof uses all of ZFC.  That is not an
issue to me.

Are such statements known?  Is there some easy way to find them?

thanks, Colin

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