# Enayat Models of Peano Arithmetic

@article{AbdulQuader2018EnayatMO, title={Enayat Models of Peano Arithmetic}, author={A. Abdul-Quader}, journal={J. Symb. Log.}, year={2018}, volume={83}, pages={1501-1511} }

Simpson showed that every countable model $\mathcal{M} \models \mathsf{PA}$ has an expansion $(\mathcal{M}, X) \models \mathsf{PA}^*$ that is pointwise definable. A natural question is whether, in general, one can obtain expansions of a non-prime model in which the definable elements coincide with those of the underlying model. Enayat showed that this is impossible by proving that there is $\mathcal{M} \models \mathsf{PA}$ such that for each undefinable class $X$ of $\mathcal{M}$, the expansion… CONTINUE READING

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