[FOM] strong hypotheses and the theory of N

Aatu Koskensilta Aatu.Koskensilta at uta.fi
Tue Mar 16 15:12:58 EDT 2010

Quoting joeshipman at aol.com:

> A related question: is there a natural way to represent the
> "arithmetical content" of ZF by arithmetical axioms; in other words, a
> natural decidable set of arithmetical statements which have the same
> arithmetical consequences as ZF?

No. It follows from the reflexivity of ZF(C) that the set of its  
arithmetical consequences is not axiomatizable by a finite number of  
schemata in the language of alpha-th order arithmetic for any set  
theoretically definably alpha.

Aatu Koskensilta (aatu.koskensilta at uta.fi)

"Wovon man nicht sprechen kann, darüber muss man schweigen"
  - Ludwig Wittgenstein, Tractatus Logico-Philosophicus

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