[FOM] theory of fields
Robert M. Solovay
solovay at math.berkeley.edu
Tue Jun 26 23:04:58 EDT 2007
Alas, I withdraw my claim. The trouble is that to check the validity of a
formula with n free variables (by the obvious algorithm) takes time
exponential in n. What does seem clear is that one can prove the
consistency of the theory of fields in IDelta_0 + Exp.
On Mon, 25 Jun 2007, Robert M. Solovay wrote:
> The answer to the last question is yes. Use the model that is the two
> element field.
> --Bob Solovay
> On Mon, 25 Jun 2007, Rupert McCallum wrote:
>> I have two questions. Julia Robinson proved that the theory of fields
>> and also the theory of fields of characteristic 0 are undecidable. For
>> which primes p is it known whether the theory of fields of
>> characteristic p is undecidable? Also, can the consistency of the
>> theory of fields be proved in Bounded Arithmetic?
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