[FOM] defining the integers

zahidi@logique.jussieu.fr zahidi at logique.jussieu.fr
Thu Sep 20 05:10:58 EDT 2007

Poonen's result is indeed very nice. Cornelissen and myself had previously
given a conditional improvement of Robinson's undecidability result for
the rationals.
We proved, assuming a conjecture about elliptic curves, that the
existential-universal theory of the rationals is undecidable.
>From Poonen's result (which is unconditional!) it follows that the
universal-existential-universal theory is undecidable.
Our paper can be found at

Best regards

Karim Zahidi

Le Ven 31 août 2007 18:07, Dave Marker a écrit :

> Bjorn Poonen has recently given a nice improvement of Julia Robinson's
> result that the integers are definable in the field of rational numbers.
> Robinson's definition was Pi_3. Poonen improves this to Pi_2 (2 universal
>  followed by 7 existential).
> A preprint of his result is on his webpage.
> Dave
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