[FOM] Weak independent statements of arithmetic

William Tait williamtait at mac.com
Tue Feb 23 15:58:43 EST 2010

I am assuming that 'same consistency strength' means that in some weak system  of arithmetic, the consistency statements can be proved equivalent. (Providing that ZFC is consistent), an example is the Rosser sentence for ZFC. 


On Feb 23, 2010, at 7:34 AM, Colin McLarty wrote:

> 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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