[FOM] Set theories mutually interpretable with n-th order arithmetic

Colin McLarty colin.mclarty at case.edu
Sat Jul 28 08:45:52 EDT 2012

Since Harvey put me on the track of using ZF[n] in foundations of
cohomology, a lot of people have given me a lot of help with it and it
is working really well.  But published sources on it are sparse.  So
far as i can find there is no published proof that ZF[n] (ZF with
powerset restricted to n successive power sets of the natural numbers}
is mutually interpretable with Z(n+2) (n plus 2 order arithmetic).

So I have put a note with proofs of basic theorems of ZF[0] and a
proof of the intepretability of ZF[n] in Z(n+2) on the math arXiv,
together with a corresponding proof for categorical set theory.  It is
arXiv:1207.6357v1, titled "Set theories mutually interpretable with
n-th order arithmetic."


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