Recently I'm thinking about question below, but I can not prove or disprove it.



> 
> Is it true that for every model $M\models I\Delta\_0$ there exists a
>  model $M'\models PA$ such that $M'$ is end extension of $M$?
> 
> 
> 


How can this statement be proved or disproved?


Thanks.



End Extension models of $I\Delta_0$
It's not true, because perhaps the model of $I\Delta\_0$ satisfies $\neg\text{Con}(I\Delta\_0)$. Since PA proves the consistency of the bounded induction principles, there can be no model of PA that has such a proof in it.


