[FOM] strong hypotheses and the theory of N
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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